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Pritzl has been accepted towards fulfillment of the requirements for PhD Astrophysics degree in , f: / .1 fl ' /// // , 4 k r": ‘ “r1741“. - -' ‘ 11/] 7"" - Major professor Date 8/4/00 MS U i: an Affirmative Action/Equal Opportunity Institution 0-12771 PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. MAY BE RECALLED with earlier due date if requested. DATE DUE DATE DUE DATE DUE 11/00 e/CIFIC/DatoDmpBS-p.“ AN EXAMINATION OF THE VARIABLE STARS IN THE UNUSUAL, METAL-RICH GLOBULAR CLUSTERS NGC 6388 AND NGC 6441 By Barton J. Pritzl A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics and Astronomy 2000 ABSTRACT AN EXAMINATION OF THE VARIABLE STARS IN THE UNUSUAL, METAL-RICH GLOBULAR CLUSTERS NGC 6388 AND NGC 6441 By Barton J. Pritzl BV photometry of the metal-rich globular clusters N GO 6388 and NGC 6441 is presented. A method for processing the images and for detecting variables is given in detail. An investigation of the color-magnitude diagrams shows an unusual blue extension to the horizontal branches in each cluster extending though the instability strip as first noted by Rich et al. (1997). The individual properties of the variable stars are discussed for each globular cluster. The periods of the fundamental mode RR Lyrae are shown to be unusually long compared to field stars of similar metallicity, implying that the RR Lyrae stars in NGC 6388 and NGC 6441 are unusually bright for their metallicity. In comparison to other Galactic globular clusters, neither NGC 6388 nor NGC 6441 fit within the standard Oosterhoff classification scheme. The mean periods of the fundamental mode RR Lyrae in both NGC 6388 and NGC 6441 are found to be longer than the typical Oosterhoff Type II cluster. A few unusually long period first overtone RR Lyrae are also detected, resulting in a smaller than expected period gap between the shortest period fundamental mode RR Lyrae and the longest period first overtone RR Lyrae. A number of RR Lyrae both brighter and redder than the horizontal branch RR Lyrae are found in NGC 6441, but they may be a product of blending with stars of redder color due to the high stellar concentration found in each cluster. Reddening determinations for each cluster are also pre- sented. Four Type II Cepheids were discovered in NGC 6388, making it the most metal-rich globular cluster known to contain such stars. Metal-rich RR Lyrae are generally believed to be relatively faint. Since the RR Lyrae in these clusters appear to be both metal-rich and very bright, this correlation of metallicity and luminos- ity does not apply. There can therefore be no universal relationship between the metallicity and the luminosity of RR Lyrae variables. To my family, especially my wife, Sara, and daughter, Alyssa. Your love and support has made all of this possible. iv ACKNOWLEDGMENTS I would like to thank my advisor, Dr. Horace Smith, for all the help and guidance he has given me over the past few years. I would also like to thank Drs. Allen Sweigart and Marcio Catelan for sharing their knowledge and insights. Thank you to my guidance committee members, Suzanne Hawley, Timothy Beers, Mark Dykman, and Joey Huston for you comments and suggestions. I would also like to thank all who helped in getting the reduction programs to work, espe- cially Peter Stetson, Nancy Silbermann, and Brian Sharpee. Special thanks to Jason Biel for helping with the images and Dave Bercik for the use of the LaTeX template. Also, thank you to all of the friends I have made here at MSU. You all helped make this experience more enjoyable. TABLE OF CONTENTS LIST OF TABLES viii LIST OF FIGURES x 1 INTRODUCTION 1 2 DATA PROCESSING 8 2.1 Observations ................................ 8 2.2 Reductions ................................. 9 2.3 Standard System ............................. 17 2.4 Comparison of Photometry ........................ 25 2.4.1 NGC 6388 ............................. 25 2.4.2 NGC 6441 ............................. 26 3 COLOR-MAGNITUDE DIAGRAMS 29 3.1 NGC 6441 ................................. 29 3.2 NGC 6388 ................................. 32 3.3 Comparisons ................................ 34 4 VARIABLE STARS IN NGC 6441 35 4.1 Discovery of New Variable Stars ..................... 35 4.2 RR Lyrae stars .............................. 38 4.3 Notes on Individual RR Lyrae ...................... 50 4.4 “Red” RR Lyrae ............................. 55 4.5 Reddening ................................. 56 4.6 Eclipsing Binaries and LPVs ....................... 59 4.7 Suspected Variable Stars ......................... 61 5 VARIABLE STARS IN NGC 6388 62 5.1 Discovery of New Variable Stars ..................... 62 5.2 RR Lyrae stars .............................. 64 5.3 Notes on Individual RR Lyrae ...................... 72 5.4 Reddening ................................. 77 5.5 Cepheids .................................. 78 5.6 Eclipsing Binaries and LPVs ....................... 79 vi 6 ASPECTS OF THE RRc AND CEPHEID VARIABLES 6.1 RRc variables ............................... 6.2 Comparisons to Long Period RR Lyrae in w Centauri ......... 6.3 Cepheids .................................. 7 CLASSIFICATION OF N GC 6388 AND NGC 6441 7.1 Introduction ................................ 7.2 Oosterhoff Classification of NGC 6388 and NGC 6441 ......... 7.3 The Luminosity of the RR Lyrae Stars ................. 7 .4 Discussion ................................. 8 SUMMARY AND CONCLUSIONS A ADDITIONAL TABLES B ADDITIONAL FIGURES vii 81 81 84 85 90 90 91 98 100 102 104 145 2.1 2.2 4.1 4.2 4.3 4.4 4.5 4.6 5.1 5.2 5.3 5.4 5.5 5.6 7.1 A.1 A2 A3 A.4 A5 A6 NGC 6388: NGC 6441: NGC 6441: NGC 6441: NGC 6441: NGC 6441: NGC 6441: NGC 6441: NGC 6388: NGC 6388: NGC 6388: NGC 6388: NGC 6388: NGC 6388: LIST OF TABLES Mean Differences in Photometry .............. Mean Differences in Photometry .............. Locations of Discovered Variable Stars ........... Mean Properties of RR Lyrae ............... Fourier Values ........................ Reddening Determinations ................. Mean Properties of Binary Stars .............. Mean Properties of Suspected Variables .......... Locations of Discovered Variable Stars ........... Mean Properties of RR Lyrae ............... Fourier Values ........................ Reddening Determinations ................. Mean Properties of Cepheid Stars ............. Mean Properties of Binary Stars .............. Cluster PrOperties ............................. NGC 6388: NGC 6388: NGC 6388: NGC 6441: NGC 6441: NGC 6441: Comparison of Photometry with Alcaino. ......... Comparison of Photometry with Silbermann et al. Comparison of Photometry with HST ............ Comparison of Photometry with HST ........... Comparison of Photometry with Hesser & Hartwick . Photometry of the Variable Stars (V) ........... viii 27 27 36 40 49 58 60 61 63 66 70 78 79 80 91 105 106 112 112 113 114 A.7 N GC 6441: Photometry of the Variable Stars (B) ........... 124 A8 NGC 6388: Photometry of the Variable Stars (V) ........... 134 A9 NGC 6388: Photometry of the Variable Stars (B) ........... 139 ix 1.1 1.2 3.1 3.2 4.1 4.2 4.3 4.4 5.1 5.2 5.3 5.4 5.5 5.6 6.1 6.2 7.1 7.2 LIST OF FIGURES A plot of the variability index versus magnitude for NGC 6388. A typical growth curve for a local standard star ............. NGC 6441 Color-Magnitude Diagrams. ................. NGC 6388 Color-Magnitude Diagrams. ................. Color-magnitude diagram showing the location of the RR Lyrae in the field of NGC 6441. .......................... Light curves for the N GC 6441 variables ................. A plot of the Fourier parameters R21 versus (1)21 for N GC 6441. . . . . Period-amplitude diagram for NGC 6441 ................. Color-magnitude diagram showing the location of variables in the field of NGC 6388. ............................ Light curves for the NGC 6388 variables ................. Plot of the Fourier parameters R21 versus $21 for NGC 6388 ...... Period-amplitude diagram for NGC 6388 ................. Nightly light curves for V35 ........................ A plot of the magnitudes for V37 versus the heliocentric Julian dates for the observations. ........................... A plot of the Fourier parameters for RR Lyrae in w Centauri. Period-amplitude diagram for the first overtone RR Lyrae in w Centauri. Mean period vs. [Fe/H] diagram comparing NGC 6388 and NGC 6441 to Oosterhofl I and Oosterhoff II globular clusters ......... Period histograms for M15, M3, NGC 6388, and NGC 6441. ..... 15 21 30 33 39 41 48 50 65 67 71 72 74 75 86 87 92 94 7.3 Period-amplitude diagram for the ab-type RR Lyrae variables of NGC 6388 and NGC 6441 as compared to field RR Lyrae of [Fe/ H] 2 -0.8 and RR Lyrae from other Galactic globular clusters ........... 95 B1 The field of NGC 6441 ........................... 146 B.2a The southeast quadrant of NGC 6441. ................. 147 B.2b The northeast quadrant of NGC 6441. ................. 148 B.2c The northwest quadrant of NGC 6441. ................. 149 B.2d The southwest quadrant of N GC 6441. ................. 150 B.3a The core region of NGC 6441. ...................... 151 B.3b The core region of NGC 6441. ...................... 152 B.3c The core region of NGC 6441. ...................... 153 B.3d The core region of NGC 6441. ...................... 154 B.3e The core region of NGC 6441. ...................... 155 B4 The field of NGC 6388 ........................... 156 B.5a The southeast quadrant of NGC 6388. ................. 157 B.5b The northeast quadrant of N GC 6388. ................. 158 B.5c The northwest quadrant of NGC 6388. ................. 159 B.5d The southwest quadrant of NGC 6388. ................. 160 B.6a The core region of NGC 6388. ...................... 161 B.6b The core region of NGC 6388. ...................... 162 B.6c The core region of NGC 6388. ...................... 163 xi Chapter 1 INTRODUCTION Globular clusters are important tools in understanding the origin of galaxies. It is the belief that these systems formed during the early stages of the Milky Way Galaxy’s formation. The stars in globular clusters are not only coeval, but also form at nearly the same location, probably from a common initial gas cloud. They thus not only give us an estimate of the age of the Galaxy, but also of its early chemical composition. In the long time Galactic globular clusters have been studied, it has been seen that the main parameter governing the morphology of horizontal branches (H83) in globular clusters is the metallicity of the cluster. Canonical metal-rich globular clusters (GCs), such as 47 Tuc, have stubby-red horizontal branches whereas metal-poor GCs, such as M15, have blue HBs. Yet, it has long been known that some GCs, particularly those with intermediate metallicities, do not show a perfect correlation between HB morphology and [Fe/ H], requiring that at least one other parameter besides metallicity helps to determine the color distribution of stars on the HB (Sandage & Wildey 1967; van den Bergh 1967). This so-called second parameter effect has been often thought to be due to age differences among the globular clusters (see Lee, Demarque, & Zinn 1990). Two clusters with similar metallicities, but which have a significant age difference between them, will exhibit a difference in their HB morphology, all else being equal. A younger GC will have a redder HB morphology for a given metallicity, while the older GC will exhibit a bluer HB morphology, since in it, the stars now reaching the horizontal branch will have a lower mass. Although the explanation for this effect is uncertain, it is either due to simply the turnoff mass being lower or because of more mass loss occurring on the red giant branch for older stars (Fusi Pecci & Renzini 1975, 1976). It should be noted that there have been other possible causes given to explain the differences in HE morphology, such as mass loss, helium abundance, CNO abundances, or rotation (Fusi Pecci & Bellazzini 1998). One particular feature about the second parameter effect has been that it had never been seen in metal-rich GCs. Armandroff & Zinn (1988) determined the metal abundances of NGC 6388 and NGC 6441 to be [Fe/ H] = -0.60 and -0.53, respectively, making them slightly more metal-rich tha n 47 Tucanae on their metallicity scale. Therefore, one would have expected the color-magnitude diagrams of N GO 6388 and NGC 6441 to show the stubby red horizontal branches typical of metal-rich globular clusters, such as 47 Tue. Until recently, very little photometry had been obtained for NGC 6441 due to the relative faintness of the stars associated with the cluster, its high degree of central concentration, and the high contamination of the field by stars belonging to the Galactic bulge. Hesser & Hartwick (1976) created a color magnitude diagram (CMD) of NGC 6441 using photoelectric and photographic data, but any meaningful results were hampered by the previously stated problems and their diagram extended only to the level of the HB. They did find two stars which they felt could be RR Lyrae candidates due to discrepancies in their measurements on a few plates. 2 NGC 6388 had been studied in somewhat more detail than NGC 6441. Alcaino (1981) provided the first B,V CMD using photographic data. A flattened giant branch and stubby red horizontal branch (HB), similar to 47 Tucanae, was seen. Although a few blue stars were seen around the HB, Alcaino was uncertain of their membership. A total of 12 variables were known in the region of NGC 6388, 9 from the catalogue of Sawyer-Hogg (1973) and 3 from Lloyd Evans & Menzies (1977). Hazen and Hesser (1986) were the first to discover RR Lyrae variables in this cluster, making NGC 6388 the cluster of highest metallicity to contain this type of variables. Of the 14 new variables they discovered, 4 were listed as probable cluster RR Lyrae with an additional 2 being candidate RR Lyrae. Silbermann et a1. (1994) obtained B,V,R CCD photometry of NGC 6388 in hope of better examining the crowded variables and obtaining a new CMD. Using three nights of observing, 3 new RR Lyrae were found, 2 probable cluster members and one field, along with 4 suspected short—period variables. Due to the short observing run and poor seeing, Silbermann et a1. were unable to clearly establish which variables are members of NGC 6388 and whether the cluster contains a small blue horizontal branch component. It wasn’t until a survey done by Rich et al. (1997), using the Hubble Space Telescope, that detailed color-magnitude diagrams of the two metal-rich clusters, NGC 6441 and NGC 6388, were obtained. Not only did they exhibit the stubby red horizontal branch associated with canonical metal-rich globular clusters, but they also showed a pronounced blue component, which extends across the location of the instability strip. Rich et a1. suggested that one possibility for this feature is that NGC 6441 and NGC 6388 are older than typical metal-rich globular clusters. Alternatively, 3 they suggested that there could be stellar interactions within the cluster. Tidal collisions may act in a way as to enhance the loss of envelope mass and lead to a bluer horizontal branch. NGC 6441 and NGC 6388 are known to be among the highest in central surface brightness and velocity dispersion among Galactic globular clusters (Pryor & Meylan 1993; Djorgovski 1993). This gives an indication that these clusters have very high central stellar densities and hence high rates of stellar interations. Yet, in conclusion, Rich and collaborators could not put forward a definitive explanation for the unusual nature of the horizontal branches in these two clusters. Examining the horizontal branches of NGC 6441 and NGC 6388, Sweigart & Catelan (1998a) noticed that in addition to the unusual blueward extension of the hor- izontal branch, there was a pronounced upward slope in decreasing B — V. It should be noted that a similar slope was found in the red clump of the HB (Piotto et a1. 1997). Sweigart & Catelan (1998b) constructed simulations of the color-magnitude diagrams of metal-rich globular clusters to test various theoretical scenarios which might account for the unusual HB morphology of the two clusters. They showed that neither of the two most accepted second parameter effects, differences in age at similar metallicity and increased RGB mass loss, nor differential reddening, could explain the morphology of the horizontal branches in the CMDs of NGC 6388 and NGC 6441. The problem is that while greater cluster age or RGB mass loss can ac- count for the blue extension to the horizontal branch, they cannot explain the extent to which the horizontal branch is SIOped. Therefore, these clusters could provide an important clue to the nature of the second parameter effect. With canonical theory unable to explain the nature of the horizontal branches 4 of NGC 6441 and NGC 6388, Sweigart & Catelan arrived at three noncanonical scenarios in order to take into account the sloped nature of the horizontal branches. The first scenario suggests that the globular cluster initially formed with a high helium abundance which leads to longer blue loops during a star’s HB evolution. This causes the HB star to reach higher effective tempertures and luminosities. Another scenario proposes that internal rotation of a star during the red giant branch phase can delay the helium flash. The two consequences of this are to increase the helium-core mass, therefore leading to a higher horizontal branch luminosity, and to increase the mass loss near the tip of the RGB giving a smaller HB enve10pe mass. The total effect of this is to again move the star to higher effective tempertures and luminosities on the HB. Finally, Sweigart and Catelan proposed the possibility of deep mixing near the tip of the RGB. This would increase the amount of helium in the envelope of the star allowing the luminosity of the RGB tip to increase. With the star spending more time along the RGB, the amount of mass loss is increased. Therefore a star will arrive both brighter and hotter on the horizontal branch as compared to a star in a cluster where this effect is not taking place. Each of these scenarios is sufficient in explaining both the blue extension to the HB and its sloped nature. Sweigart (1999) suggested an additional scenario: Some heavy elements might form dust grains which are then removed from the enve10pe by radiation pressure at the tip of the red giant branch (RGB), leaving the gas metal depleted. The overall metal abundance of the envelope can then be reduced if the metal depleted gas can be convectively mixed throughout the envelope. One would then expect a HB star to be both bluer and brighter, and have lower [Fe/ H] than the cluster. 5 ——- .p—a—v-—~ One result to come from each of the models is the fact that the horizontal branches of these two clusters would need to be unusually bright for their given metallicity. An important test of this idea requires us to seek any RR Lyrae stars (RRLs) in these clusters. The idea behind this is the fact that, if the HE is unusually bright, then the RRL should have unusually long pulsation periods. This can be seen by applying Ritter’s equation, Pfi = Q, where P is the pulsation period of a star, p is its mean density, and Q is the pulsation constant. If the luminosity of a star increases, it will be less dense due to the increase in radius and therefore the period must increase in order for the product to remain constant, assuming a constant mass and effective temperature. One needs to compare the periods of any RRL found in these clusters to other RRL of similar metallicity to see if they are indeed unusually long. An initial comparsion was done by Sweigart & Catelan (1998b; Figure 3) using the two known fundamental mode RRL in NGC 6388 (Silbermann et a1. 1994). Using a period—temperature diagram they showed that the two RRL did appear to have longer periods compared to field RRL of similar metallicities at a given temperature. Recently, surveys were initiated by Andy Layden and collaborators of globular clusters in which few variables have been found. Layden et al. (1999) used ground based V and I photometry to study the color-magnitude diagram and variable star population of NGC 6441. Layden et a1. discovered about 50 new variable stars in the vicinity of NGC 6441 including 11 RRLs which are probable members of the cluster and 9 other suspected short period variables, some of which might be RRL. They also found that the two candidate RRL found by Hesser & Hartwick (1976) showed 6 mw-‘A—I no variability. The fundamental mode RR Lyrae stars which were probable mem- bers had unusually long periods. Their locations in the period—amplitude diagram (Figure 9 of Layden et a1.) were consistent with the models of Sweigart & Catelan (1998b), implying that the RRLs were indeed unusually bright. Layden et al. also found a normal ratio of HB stars to red giant branch stars, implying that the helium abundance of NGC 6441 was not extraordinarily high, and indicating that the high helium abundance scenario was not correct. This thesis reports new B and V photometry of NGC 6388 and NGC 6441 which has led to the discovery of additional variable stars. Results of this study are presented in detail and call attention to several unusual properties of the RRLs, e.g. unusually long periods, in these two clusters and of the clusters themselves. Chapter 2 DATA PROCESSING 2. 1 Observations Observations were obtained with the 0.9m telescope at CTIO using the Tek 2K No. 3 CCD detector. The 2048x2048 CCD has a field size of 13.5 arcmin per side with a pixel size of 0.40 arcsec per pixel. The CCD was read out through all four amplifiers simultaneously using an Acron CCD controller. Images were obtained on the UT dates of May 26, 27, 28, and 29 and June 1, 2, 3, and 4, 1998. The gap allowed us to have a longer baseline for observing the variables in order to have more complete coverage for the light curves. The seeing ranged from 1.1 to 2.5 arcsec, with the typical seeing being 1.4 arcsec. Exposures of each cluster were taken in V and B with exposure times of 600 seconds. Alternating observations between each cluster resulted in 8—9 images of each cluster in each filter per night on average. Images of NGC 6441 were centered 4 arcmin east of the cluster center to avoid including a bright foreground star within the field. Landolt (1992) and Graham (1982) standards stars were observed on the photometric nights, June 1, 2, and 3. A color range in B — V of 0.572 to 2.326 mag and airmass of 1.035 to 1.392 was covered. Sky flats were taken on nights 1, 2, 4, 5, and 6. 2.2 Reductions A detailed procedural outline is given in the following sections. Although there are a number of references for the programs used below and some manuals outlining the procedures, these existing writings are not, in themselves, complete. Therefore, where the steps were previously incomplete, a more detailed account is given. Italicized text indicates prompts given by a program. It is hoped that this account will assist other users of these reduction programs. The raw CCD images were initially processed following the IRAF cookbook (Massey 1997). The images were corrected for bias followed by flat-field division. The flats were created using short exposures of the twilight sky, which were then combined, using the z'mcombz'ne routine in IRAF, into one master flat for each filter. After examining the flats with implot to detect variations in the images, it was found that the top 12 rows jumped in counts significantly enough to trim them from all the images using hedz't in IRAF. The images were reduced using the stand-alone packages created by Peter Stet- son: DAOPHOT II, ALLSTAR, and ALLFRAME (Stetson 1987; Stetson 1994). The number of images of each cluster for each filter ranged from 42 to 48. Following the steps in the User’s Manual for DAOPHOT II created by Peter Stetson (1998), a script was created to run the reduction programs, DAOPHOT II and ALLSTAR, in order to advance from obtaining aperture photometry to profile-fitted photometry. The input consisted of the image to be reduced, the full width at half maximum of a stellar image, and the fitting radius, which differed from frame to frame due to seeing variations and variations across the frame. It should be noted that coma was seen on the images which also distorted point source image profiles, most noticeably in the corners of the frames. Also input were the :c and y offsets of each image from a fiducial frame, which was selected by choosing the frame with best seeing. The stars used to create the point-spread function (PSF), which was used to obtain the profile-fitted photometry in ALLSTAR, were isolated stars chosen on the fiducial frames for each cluster and each filter. A program was then run to find these stars in each image and use those stars to create the PSF for each frame. Once the stars were picked and the PSF created, neighboring stars were subtracted off using ALLSTAR. This subtracted image was then used by DAOPHOT II to create a cleaner PSF. This time the PSF was allowed to vary across the frame since, as stated before, stars were being distorted by coma the further one went out from the center of the frame. Once more, any neighboring stars were subtracted. Before creating the final PSF, any potential PSF stars with X 2 0.045 were excluded, where X is the rms residual of the actual brightness values contained within circles of radius one fitting radius about the centroids of the PSF stars compared to that expected from the PSF profile. Certain exceptions had to be made in the cases where the overall seeing was poor for a frame. For those frames, the lower limit to the x value was increased. This allowed more PSF stars to be included in the final PSF calculation. In the final run of ALLSTAR, all suitable stars on each frame were reduced. Once all the images were reduced in this way, a montaged image was created from all the images using Stetson’s package MONTAGE II. The purpose of creating a montaged image is to create a master star list containing as many stars as possible 10 from all frames, since the frames may be offset from one another. In preparing to run MONTAGE II, good positional transformations between each frame are needed. This can be done using Stetson’s programs DAOMATCH and DAOMASTER. The program DAOMATCH matches up the frames to a fiducial frame by looking at the brightest stars and trying to match them up. The fiducial frame is the frame to which all other frames will be standardized. Typically it is the frame with the best seeing. The input for the program is the photometry file for each frame starting with the one for the fiducial frame. It is better to use the profile-fitted photometry outputted by ALLSTAR (.als) than the aperture photometry from DAOPHOT II (.ap) since the positions found in the profile-fitted photometry are more accurate. For each frame, it must be decided if the given transformation returned by DAO- MATCH is good enough or if the fit needs to be iterated to add more stars to create a more accurate transformation. DAOMATCH is a useful program, but it does not always work. Things like rotation between frames or large offsets can create problems for the program. Stetson states in his reduction manual (ccdpck.man, given in the DAOPHOT 11 package): “The overlap on the sky should be at least 25 to 30 percent, and the exposure times should not be such that the brightest stars in one frame are unmeasureable in the other.” In those cases, the initial coordinate transformation must be done manually, comparing the positions of stars between the frames. As stated before, the transformation equations from DAOMATCH are only ap- proximate, being based on a small subset of bright stars. To remedy this problem and to ensure that the final transformations are accurate enough, one can use DAO- MASTER. DAOMASTER, given an approximate transformation file (the .mch file 11 from DAOMATCH), cross-identifies all stars possible and refines the estimates of the transformation equations. First, input the “Minimum number of frames” in which a star must absolutely be found, the “Minimum fraction of frames” that a star should appear on, of those frames in which a star may reasonably be expected to appear, and “Enough frames” by which any star that is found on this many frames will be ac- cepted, regardless of how many frames it could have been found in. I typically would enter the values: 2-3, 0.1, 2/ 3 :1: (total number of frames). The maximum sigma by which you will accept a star’s magnitude must also be chosen (2, in my run), where sigma is the error in the mean instrumental magnitude of a star, based on a weighted average of all available observations corrected to the magnitude scale of the fiducial frame. I chose transformation equations which allowed for any rotation or scaling (value=6) of the coordinate system between frames, given in the form, $(1)=A+C*:r(2)+E*y(2) y(1)=B+D*:r(2)+F*y(2) Finally a match-up radius must be chosen in order for the cross-identification to be accurate (typical value = 2 pixels). Stars will be cross-identified only if their transformed positions agree to within the match-up radius. Once all of these inputs are given, DAOMASTER processes all of the given frames and outputs on the screen the new transformations and the total number of acceptable stars found through the limits set above. The program then asks you if 12 you would like to change the match-up radius. In order to get the most accurate transformation equations, it is best to start out with a high number for the match-up radius and reduce the number by 1 each iteration until you reach a match-up radius equal to 1. There are many output options one can chose from DAOMASTER, but for the purpose here, “A file with the new transformations?” should be chosen. Now one has an accurate global set of transformation equations between each frame. Before running MONTAGE II, one should create a seperate directory and place the transformation equation file (.mch), all of the aperture photometry files (.ap), the PSF files (.psf), and the image files (.imh) for each image in this directory. MON- TAGE 11, once run, should be given the following inputs: The “File for transforma- tions” (the .mch file), no “Image sufi‘ix” is needed (press [RTRN]), for “Minimum number of frames, percentile”, I chose for MONTAGE II to at least use 3 frames and 0.5 for the fraction of frames a star is expected to be found on in order to be included, press CTRL-D for the “X and Y limits” for MONTAGE II to chose the limits on its own, the “Expansion factor” is 1 so that there is no resizing of the frames, and answer yes to allow the program to “Determine sky from overlap”. MONTAGE II then outputs some data on the screen. Of all that is listed one needs to note the offset of the montaged frame to that of the fiducial frame and the sky values of each of the frames. The montaged image created by the program has a zero sky value. The sky values were averaged and added back on to the montaged image using the imarith routine in IRAF. The montaged image was then processed in the same way as described above from obtaining the aperture photometry through finding the PSF for the image to use in ALLSTAR. The final output (.als), using ALLSTAR on the 13 montaged image, was then used as the master star list. The coordinates of the stars were placed back to those of the fiducial frame using the offsets between the montaged image and the fiducial frame listed by MONTAGE II. The program, ALLFRAME, reduces all frames together in order to make use of the information gleaned from the frames with good seeing on the frames with poor seeing. For example, on a frame with good seeing, two companion stars may be resolved, whereas on a frame with poor seeing the stars may be blended and unresolved. ALLFRAME makes use of the fact that two stars are there and not one and will try to fit the PSF on the frame with poor seeing so as to obtain photometry for two stars. To run ALLFRAME, the file containing the transformation equations between frames, a master star list, the individual PSF files for each frame, and a file containing the read noise, gain, high and low good data values, and fitting radius for each frame need to be input. The first three of these have already been created. The final input was created using ALLSTAR. ALLSTAR was run inputting the fitting radius, the appropriate .psf and .ap files for each frame, and then pressing CTRL- C at the subtracted image prompt in order to interrupt the program. This allows the header of the ouput .als file to contain the necessary information listed above. ALLFRAME was then run with these inputs. ALLFRAME outputs a photometry file (.alf) for each frame for each star found in that frame. In order to place the instrumental magnitudes on one system and perform an initial variable search, the output .alf files from ALLFRAME were run through DAO- MASTER. Following the steps outlined previously for DAOMASTER, except for choosing 1 for the match-up radius immediately and changing the file extensions 14 lO I I I I I I I I ». J 8 - _ if) ‘0 6 7 I E 3* . . E .9 . 6 4 »- — > _ 4 2 _ O 1,}. I. o ‘- l 4 Figure 1.1. A plot of the variability index versus magnitude for NGC 6388. 15 in the transformation file (.mch) from .als to .alf, DAOMASTER was run to get a file containing the mean magnitudes for each star (.mag) and a file containing the corrected magnitudes shifted to the fiducial frame for each star (.cor). From the .mag file, I was able to plot the variability index versus the instrumental magnitude. This gave an indication of which stars were variables (see Figure 1.1) . The vari- ability index is the ratio of the magnitude scatter observed to that expected from the individual standard errors, i.e., the ratio of external error to internal error. The expectation value for a star with only random noise in its photometry would be zero. Therefore, the variability index for a nonvariable star tends to zero, while a variable star has some higher positive value depending on the amplitude of the variability (Stetson 1996). The stars with higher variability index than the apparent noise were chosen as candidate variables. A program was created in order to list the identifica- tion number, coordinates, and mean magnitude of the candidate variables from the .mag file once a cut-off level was determined (2 was the cut-off for this study). Once candidate variables were chosen, another program was created to collect the data for each star in that list from the .cor file. Given the dates of the observations and the location of the object, heliocentric julian dates (HJDs) were found for each frame using the rucorrect command in IRAF. A file created by combining the data for each star with their HJD was then used in the phase dispersion minimization (PDM) rou- tine (Stellingwerf 1978) in IRAF to check the variability and when possible, create the best light curve, and find the period of the star. This routine tries to minimize the dispersion of the data at a constant phase in order to find the best period. This is done by finding the minimum in the ratio of the overall variance for all the samples 16 of the data to the variance of the magnitudes for a given period. 2.3 Standard System Photometry of standard stars was obtained on three photometric nights in B and V. The standard stars were chosen from Graham (1982) and Landolt (1992). A range of colors, in B — V, (0.572 - 2.326 mag) and airmass (1.035 - 1.392) were covered. This range in color adequately covers the range spanned by the stars found in N GO 6388 and NGC 6441 especially the focus of this study, the RR Lyrae stars. This is due to NGC 6388 and NGC 6441 having reddenings on average of 0.38 and 0.53, respectively (see Sections 4.5 and 5.4). To place the photometry of the standard stars on to the standard Johnson B, V system, I followed an outline created by Dr. Peter Stetson making use of a set of programs he created (see ccdpck.man from the DAOPHOT II package and “Cooking with ALLFRAME: Photometry and the H0 Key Project”, Turner 1997). The stan- dard stars from each night were reduced seperately in order to determine any nightly variance. No significant differences from night to night were observed. To ensure that photometry of the standard stars is not contaminated by any neighboring stars, all stars except the standard stars are subtracted off the image. A PSF for each frame was found in the same manner as described under Section 2.2. Each frame was then run through ALLSTAR to determine accurate positions. A file containing the positions of the standard stars is created from the list of PSF stars obtained by the option pick in DAOPHOT II. The output subtracted image is then used to obtain aperture photometry of the standard stars. The photometry is found for a series of 17 apertures of increasing radii. Stetson suggested a formula for the best set of aperture radii: 5 = (OR — IR) /99 ap1= IR ap2=ap1+4*6 ap3=ap2+5=i=6 ap12 = ap11+14*6= 0R where OR is the outer radius and IR is the inner radius of the apertures. I chose IR and OR to be 1.5 and 15, respectively, with the inner sky radius at 20 and the outer sky radius at 35. The aperture photometry was then fed into a program, DAOGROW (Stetson 1990), which would create growth curves for each of the stars showing how the magnitude within the aperture changes as a function of the adopted aperture size. The equation used to describe the general stellar profile is I(r,X,-;R,-,A,B,C,D,E)= (B+E-X,-)-M(r;A)+(1—B—E-X,-) -[C-G(r;R,-)+(1— C) ' H(r;D-R,)], 18 where r is a radial distance measured (in pixels) from the center of the concentric apertures which are in turn assumed to be concentric with the star image; X,- is the airmass of the ith data frame (known a priori); R,- is defined as the seeing— (guiding-, defocusing- ) related radial scale parameter for the ith data frame; and M, G, and H are Moffat, Gaussian, and exponential functions, respecively: G(r;R,:) : e$p(—r2/2R,2) 1 27TR,2 Hm D - R.) = ,7, ,),exp[(—r/(D * a») 1 (D * DAOGROW was allowed to solve for A, B, and C with the last two coefficients (D and E) being set to 0.9 and 0.0. The maximum error allowed for each magnitude was set to 0.05. The purpose of this step is to use the information from DAOGROW to determine the aperture correction for each frame. The previous instrumental magnitude of a star is the magnitude that is found for the smallest aperture radius given. Due to other factors, such as atmospheric conditions or the optics of the telescope, the light from a star is not concentrated as a single point. Instead, the light is distributed in a more or less Gaussian manner. So the “extra” light that is distributed on the wings need to be taken into account. This is a critical phase. One does not want to have the outer aperture radius too small so that all of the light is not collected. One also does not want to extend the outer aperture radius too far, so that the growth curve begins to decline due to background noise. A typical growth 19 curve is shown in Figure 1.2. Next, all of the observational data are collected through another Stetson pro- gram, COLLECT. Before running COLLECT, a file containing the exposure infor- mation (.inf) for each frame needs to be created. This can be done using Stetson’s AIRMASS program. The key information needed to run this program is the observa- tory location, readout time and shutter-timing error of the CCD, the image header keywords for RA, DEC, equinox, filter, date, UT, and exposure time, along with the photometry file. The program takes this data and outputs a file containing the airmass terms for each frame, the mid-exposure times, and Julian dates. For reasons as yet to be determined, the airmasses were not calculated correctly and needed to be re-entered by hand. Another file needed for these reductions contains the IDs and the positions of the standard stars for the fiducial frame (.fet). This file was created by copying the profile-fitted photometry from the .als file of the fiducial frame for each of the standard stars. With these files along with filter labels, time of effective midnight, and the file with positional transformations (.mch), COLLECT was run. It should be noted that within the .mch file, the first file listed needs to be the .fet file. Since this file was created from the fiducial frame, one only needs to copy the transformation for the fiducial frame. The main information needed by COLLECT were the output files for each frame from DAOGROW that contained the total mag- nitudes for each star (.tot). Using the stars with total magnitudes in the .tot file, COLLECT finds the corresponding stars in the .alf file for that frame and computes the additive magnitude correction to place the relative profile-fitted magnitudes on an absolute system of the large-aperture photometry. 20 Am 5 , , lO Aperture Rodlus (pixels) Figure 1.2. A typical growth curve for a local standard star. 21 15 Before creating the equations to transform the instrumental magnitudes to the standard magnitudes, a file is needed listing the standard magnitudes of the standard stars (.lib). Stetson’s CCDLIB program allows the standard magnitude and error to be entered for up to six photometric indices. All data for the standard stars were taken from Landolt (1992) and Graham (1982). The program, CCDST D, then takes this data, and the output from COLLECT, and by least-squares computes the transformation and extinction coeflicients used in going from the instrumental to the standard system. The transformation file needed by the program has the form: Ii 2 a linear function of standard magnitudes Mj Oi 2 Mi + a linear function of product of standard indices Ij, airmass, time, and fitting coefficients For example, in this study the form of the equations used was: Il=M1 I2=M2—M1 01=M1+A0+A1*IZ+A2*X+A3*I2*12+A4*I2*X+A5*T 01=M2+BO+Bl*I2+B2*X+B3*I2*12+B4*I2*X+B5*T where M1 is V, M2 is B, X is the airmass term (actual airmass — 1.25), and T is 22 the Universal Time from midnight. When trying to make the transformations from one system to another, CCDSTD lists the stars whose residuals are two standard errors or larger. All of these stars were systematically removed each iteration until no more were listed. After trying different forms of the transformation equations the final equations were set as: v = V — 0.003(B — V) + 0.125X — 0.007(B — V)2 + 0.064(B — V)X + 0.005T + CV b = B + 0.121(B — V) + 0.24OX — 0.010(B — V)2 + 0.064(B — V)X + 0.005T + CB where CV and CB are the zero point offsets for the V and B magnitudes, respec- tively. A total of 24 standard stars were used in the transformations. Comparing the transformed magnitudes of the standard stars with the values given by Graham and Landolt shows rms residuals of 0.010 magnitudes in V and 0.012 magnitudes in B. Since the cluster field contains thousands of stars, it is possible to create a set of local standard stars, transform them to the standard system, and use these to transform the rest of the stars in the frame to the standard system. Seventy- one and fifty-seven local standard stars were chosen for NGC 6388 and NGC 6441, respectively. These stars were put through the same steps as the standard stars listed above up to the point of using CCDSTD for B and V. To transform the instrumental magnitudes of the local standards to the standard B, V system, the Stetson program CCDAVE is used. Before running the program, the library file (.lib) must be edited to include the IDs for the local standards along with those for 23 the standards stars. In addition to this file, CCDAVE needs the files containing the observational magnitudes for the stars (.obs, from COLLECT) to run. The program must be told to include non-library stars for the local standard stars to be transformed to the standard system. Now that the local standards have been placed on a standard system, the rest of the stars in the CCD image can be reduced. The library file must now be editted to include only the standard magnitudes for the local standards. With the .alf files being the source of the photometry used in transforming the instrumental magnitudes to standard magnitudes, the IDs and positions of the local standards in the .fet file must be changed from those given in the .als file to those given in the .alf. A file containing the image pairs and the weight to be given that pair must be created. In this case, the ratio is 0.8 for V to B. A file containing the information as to where each star in the fiducial frame appears in each of the other frames can be created from one of the outputs of DAOMASTER (“A file with the transfer table .9”; .tfr). The .inf file must also be expanded to contain the information for all the frames in each filter. With these files, Stetson’s TRIAL can be run. This program will calculate and apply aperture corrections, convert instrumental magnitudes to the standard system, find the weighted mean magnitude for each star over all epochs, and look for variable stars, outputting files containing magnitudes at each individual epoch for each variable candidate. TRIAL also has the ability to detect variable stars using the variable star search algorith outlined by Stetson (1996). To search for variables, TRIAL needs to know the limits on variability, weight, period, and magnitude. The values 2, 1, 0.01, and 21 were used to give the lower limits for the variability index, 24 the period, and magnitude, and the percentage of the stars found in that range to be analyzed. It should be noted at this point that TRIAL was designed to make use only of V and I bands. It will calculate and output V light curves, but not B. To get around this, the program as it is written needs to be fooled. All indices in each necessary file (.tfr, .fet, .inf, .lib, and .clb) were switched around so that B was in the V place and V was in the B place. This allowed the program to detect and output the necessary B light curve data. TRIAL was able to detect a majority of the variables already found previously using the variability index in DAOMAST ER. Only a few long period variables were not detected. In addition, a few more variables were found using TRIAL that were not found before. It should be noted that TRIAL outputs the Modified HJDs, which were one half day earlier than the true HJD. 2.4 Comparison of Photometry 2.4.1 NGC 6388 The V and B photometry of this study on N GO 6388 was compared with the photom— etry of three earlier studies. First, our photometry was compared to the photoelectric photometry of a number of the brighter standard stars in the field of NGC 6388 ob- tained by Alcaino (1981). Alcaino reported that 11 of the 26 stars used to calibrate his NGC 6388 data were found to be in good agreement with independent obser- vations by Freeman. Table 2.1 lists the mean differences between our photometry and the photometry of previous surveys. The star-by-star comparisons against the 25 standards found by Alcaino can be found in Table A1. A large number of comparisons could be made with the CCD photometry of Silbermann et al. (1994). Using the published data (Table 3, Silberman et al.), stars were matched up by position to our data. A number of discrepant values were found. With no image to compare to from Silbermann et al., it is difficult to ascertain whether these stars were crowded or not. The majority of magnitudes were in good agreement with one another. Table AZ list the magnitudes of the stars leaving out the stars with greatest discrepancies (errors > 0.20 mag). A comparison to the HST B, V photometry obtained by Rich et a1. (1997) of NGC 6388 was also made. Due to the compact nature of NGC 6388 it was difficult finding a large number of uncrowded stars on the images obtained at CTIO (our typical seeing was 1.4 arcsec) to compare with those found using the HST data, which looked only at the inner regions of the cluster. The photometry for 9 of the less crowded stars is listed in Table A3 for comparison. It is seen in Table 2.1 that our photometry, on average, tends to be brighter by a few hundreths of a magnitude. The reason for such a discrepancy is uncertain. It may be the case that a large enough sample of comparison stars was not taken for the Alcaino and HST comparisons, since the larger comparison data set from Silbermann et al. shows a good agreement. 2.4.2 NGC 6441 The photometry of stars in the NGC 6441 field could be compared with photometry in three earlier studies. Table 2.2 lists the mean differences in photometry between 26 Table 2.1. N GC 6388: Mean Differences in Photometry Reference AV AB Alcaino 0.060 :l: 0.011 0.033 :l: 0.022 HST 0.075 i 0.010 0.034 :l: 0.013 Silbermann et al. 0.020 :l: 0.005 0.003 :1: 0.018 Table 2.2. NGC 6441: Mean Differences in Photometry Reference AV AB HST 0.043 :1: 0.014 —0.009 :1: 0.012 Hesser 85 Hartwick 0.033 :l: 0.016 0.029 :l: 0.014 Layden et a1. -0.400 :l: 0.005 our survey and previous surveys. First, our B and V photometry was compared with the B,V photometry obtained by Rich et al. (1997), from HST observations of NGC 6441. Unfortunately, even the outermost stars in the field of view of WFPC2 tended to be crowded on the images obtained at CTIO (our typical seeing was 1.4 arcsec). The comparison with Rich and collaborators is therefore based upon only 14 stars of lesser crowding. As seen in Table A.4, there appears to be agreement to within a few hundredths of a magnitude, but given the small number of stars it is diflicult to make a strong statement about the degree of agreement. A larger number of comparisons could be made with the photoelectric and pho- tographic photometry of Hesser & Hartwick (1976). In a few cases, discrepancies greater than 0.2 magnitudes were seen. However, these discrepant cases tended to be 27 red stars and the differences may be indicative of real changes in brightness of low amplitude red variable stars in the NGC 6441 field. When these few outliers were excluded, we obtained the results listed in Table A5. Finally, we compared our V magnitudes with the V photometry of Layden et al. (1999). As indicated in Table 2.2, our V photometry and that of Layden et al. are surprisingly discrepant. We have no good explanation for this discrepancy. Since our V photometry appears to be in reasonable agreement with that of Rich et a1. and Hesser & Hartwick, it may be that there is a zero-point error in the Layden et a1. photometry. Individual comparisons can be see in Tables A.4 and A5. Again, it is seen that the V photometry of this survey is slightly brighter than that of other surveys. As mentioned in Section 2.4.1, it is uncertain if this difference is real or an effect of small sampling. 28 Chapter 3 COLOR-MAGNITUDE DIAGRAMS The color-magnitude diagram (CMD) was the critical tool for the initial discovery of the unusual natures of NGC 6388 and NGC 6441. An analysis of the morphology of the CMD can provide important information on the ongoing processes occuring in the cluster and on those involved in the cluster’s formation. Comparisons to other known clusters can also lead to insights on the properties of the clusters. 3.1 NGC 6441 Figure 3.1 shows four color-magnitude diagrams obtained from our photometry of N GC 6441. The color-magnitude diagrams are constructed for stars lying at different distances from the center of the cluster. A total of 14127 stars make up the CMD in Figure 3.1a. Only the stars with values of X < 1.5 from Stetson’s TRIAL program, and which were found on 28 or more frames, were included. The effects of differential reddening can immediately be seen, especially along the red giant branch. The strong red component of the HE is evident (V ~ 18, B — V ~ 1.5) as is its blue extension. We also see many features of the field bulge population, which is particularly to be expected since our images are shifted off of the cluster center to avoid a foreground star. The main sequence of the 29 18 16 14 20 18 16 14 20 I I I (15 1 1.5 2 215 (15 1 1.5 2 1L5 B-V B—V Figure 3.1. NGC 6441 Color-Magnitude Diagrams for the stars (a) located in the complete field of view, (b) out to a radius of 1.7 arcmin and (c) out to 2.7 arcmin from the cluster center, and (d) 6-11 arcmin east of the cluster center. 30 field extends up through the cluster’s HB from about (B — V) ~ 1.2 to ~ 0.8. The field red clump, or HE, is found at V ~ 17 and (B — V) ~ 1.7. The contribution of the bulge stars to the CMD of Figure 3.1a can be seen in Figure 3.1d. Here we have plotted all stars that are 6-11 arcmin eastward from the cluster center (the tidal radius of NGC 6441 extends to 8.0 arcmin (Harris 1996)). One interesting feature on the diagrams of NGC 6441, which can also be seen in the CMDs of Rich et al. (1997) and Layden et al. ( 1999), is a small clumping of stars slightly fainter and redder than the red HB of NGC 6441 (V ~ 18.5, B — V ~ 1.5). This appears to be a luminosity function bump. Although this bump is diflicult to discern in Figure 3.1, its presence in the HST CMD makes it likely to be associated with the cluster. An investigation into its properties could give an idea as to the helium content of the cluster (Sweigart 1978; Fusi Pecci et al. 1990; Zoccali et al. 1998) Figure 3.1b is our closest approximation to the area covered by the CMD of Rich et al. (1997), including stars within a radius extending out to approximately 1.7 arcmin from the cluster center. The morphology of the HB is clearer in this figure and Figure 3.1c. Not only do we see the sloped nature of the blue extension to the HB from the red clump to the turn-off of the blue tail, but the slope in the red HE is also seen as was first noted by Piotto et al. (1997). The HB slopes from V ~ 18, atB—V~1.5,toV~17.5,atB—V~0.6. 31 3.2 NGC 6388 Figure 3.2a is made up of 19544 stars in the field centered on NGC 6388. Only stars with X 31.5 are shown. The field does not contribute as much in the CMD of NGC 6388 as in NGC 6441 since the images were centered directly on the cluster and due to the fact that NGC 6441 lies at E 2 353°, b 2 —5°, while NGC 6388 lies slightly farther from the galactic plane at E = 345.5°, b = ——6.7°. The red clump of the HB of the cluster can be seen at V N 17.2, (B - V) ~ 1.25. The main sequence of the field can be seen extending through the cluster’s HB from (B — V) ~ 1.0 to ~ 0.7. Figure 3.2d shows the contribution of the field to the CMD of NGC 6388 in Figure 3.2a. Stars were chosen from a radius greater than 5.5 arcmin from the cluster center (the tidal‘radius of NGC 6388 is 6.21 armin (Harris 1996)). As with NGC 6441, the effects of differential reddening on the red giant branch can be seen in Figures 3.2 a, b, and c. Another feature seen on the RGB is the luminosity function bump at V ~ 17.8, B — V ~ 1.3. As mentioned in Section 3.1, a closer analysis of this feature could shed light on the helium content of N GC 6388. Figure 3.2b shows all stars within 1.7 arcmin from the cluster center, giving the closest fit to the area of NGC 6388 as observed by Rich et al. (1997). Although the field contaminates the least in this figure, it is Figure 3.2c that best shows the blue extension of the HB from about (V, B -— V) of (17.0, 0.5) to (19.0, 0.3). Similar to N GO 6441, NGC 6388 exhibits a slope of about 0.5 mag can be seen from the red clump to the blue extension of the HB. 32 Figure 3.2. NGC 6388 Color-Magnitude Diagrams for the stars (a) located in the complete field of view, (b) out to a radius of 1.7 arcmin and (c) 2.7 arcmin from the cluster center, and (d) from a radius of 5.5 arcmin outward from the cluster center. 33 3.3 Comparisons Metal-rich globular clusters (GC), like 47 Tuc, typically exhibit short stubby HBs that do not extend into the instability strip. Up until the work done by Hazen & Hesser (1986) on NGC 6388, NGC 6569 was known as the most metal—rich GC to contain RRL variables at [Fe/H] = —-0.86 (Hazen-Liller 1985), excluding a single confirmed RRL in 47 Tuc. Although no CMD of N GO 6569 is available, it is evident that it must have a HB that extends blueward, not typically found in a cluster of its metallicity, which make it a good target for future study. NGC 6388 and N GC 6441 stand out from other known metal-rich globular clus- ters in that both exhibit an unusual HB that not only has a blue extension, but slopes upward in V with decreasing B — V. I therefore confirm that NGC 6388 and NGC 6441 are metal-rich globular clusters which show a second parameter effect. Unfortunately, each cluster is affected by differential reddening spreading the width of the RGB and, as we shall see, complicating the interpretation of the colors and brightness of their RRL. A red giant bump, seen both fainter and redder than the cluster’s red clump, is observed in both NGC 6388 and NGC 6441. Although the clusters exhibit similiar morphologies, there are notable differences between NGC 6388 and NGC 6441. The blue extension of the HB of NGC 6441 appears to be more populated than NGC 6388, while NGC 6388 has more of a tail on the blue extension of its HB. The effects of these differences on the variable stars found in each cluster are discussed throughout the subsequent chapters. 34 Chapter 4 VARIABLE STARS IN NGC 6441 4.1 Discovery of New Variable Stars As noted, variable stars were identified in two ways: first, Stetson’s DAOMASTER routine was used to compared the rms scatter in our photometric values to that expected from the photometric errors returned by the ALLFRAME program. Second, we applied the variable star search algorithm presented by Stetson (1996). Results from the two approaches were very similar. The time coverage of our observations is well suited for the discovery of short period variability, but not for the detection of long period variables. All of the probable short period variable stars identified by Layden et al. (1999) which were within our field were recovered during our variable star searches. In addition, 49 probable new variable stars were detected, along with 6 suspected variables. In crowded regions closer to the cluster center, the B photometry proved superior to the V photometry for purposes of identifying variable stars, presumably because of the lesser interference from bright red giant stars. Finding information for the new variable stars is given in Table 4.1, where X ,Y are the coordinates of the variables on the CCD (the cluster is assumed to be at (1635,1051)) and Aa,A6 are the differences 35 Table 4.1. NGC 6441: Locations of Discovered Variable Stars ID X Y Aa A6 V1 1514.0 1161.2 49.2 -44.3 V2 1543.2 988.5 37.5 24.2 V5 1136.0 473.8 200.1 228.5 V6 1559.6 928.4 31.0 48.1 V9 1695.5 1170.2 -23.2 -47.8 V10 1441.5 1197.1 78.1 -58.5 V37 1553.3 756.7 33.5 116.2 V38 1622.1 658.2 6.0 155.3 V39 1343.3 895.1 117.3 61.3 V40 1710.2 1189.6 -29.1 -55.5 V41 1546.0 1180.0 36.4 -51.7 V42 1637.2 817.6 0.0 92.0 V43 1523.0 911.8 45.6 54.7 V44 1598.6 1187.9 15.4 -54.8 V45 1798.8 1390.0 -64.4 -135.1 V46 1996.8 1252.3 -143.5 -80.4 V47 1452.7 1809.9 73.6 -301.7 V48 784.7 1212.0 340.3 -64.4 V49 994.8 813.5 256.4 93.7 V50 1458.4 1457.3 71.4 -161.8 V51 1273.2 611.8 145.3 173.7 V52 1723.7 833.7 -34.4 85.6 V53 1655.6 856.5 -7.3 76.6 V54 278.2 924.9 542.5 49.5 V55 1654.9 958.7 -7.0 36.0 V56 1694.4 988.7 -22.8 24.1 V57 1714.8 1028.7 -30.9 8.3 V58 1586.2 1055.8 20.3 -2.4 V59 1757.3 1119.4 -47.9 —27.6 V60 1626.7 1166.9 4.2 -46.5 V61 1585.4 1193.7 20.7 -57.1 V62 1630.6 1203.5 2.6 -61.0 V63 1688.0 1007.4 ~20.2 16.7 V64 1736.5 1057.6 -39.6 -3.1 V65 1633.2 963.3 1.6 34.2 V66 1684.5 906.7 -18.8 56.7 V67 710.3 1157.3 370.0 -42.7 V68 1981.4 1553.1 -137.3 -199.8 V69 1162.0 1102.9 189.7 -21.1 36 Table 4.1 (cont’d). NGC 6441: Locations of Discovered Variable Stars ID X Y Aa A6 V70 1889.2 1181.9 -100.5 -52.5 V71 1538.4 846.8 39.4 80.4 V72 1586.1 518.2 20.4 210.9 V73 283.7 635.7 540.3 164.2 V74 1469.8 1027.1 66.8 8.9 V75 1652.0 1139.2 -5.8 -35.5 V76 1349.6 1149.9 114.8 -39.8 V77 1130.4 1261.8 202.3 —84.2 V78 1205.4 1629.1 172.4 -229.9 V79 1607.6 1139.4 11.8 -35.6 V80 1203.9 1288.8 172.9 -94.9 V81 1509.9 382.2 50.8 264.9 V82 1801.4 619.8 -65.4 170.5 V83 866.4 743.7 307.7 121.4 V84 1753.9 1006.6 -46.5 17.0 V85 1840.5 1214.2 -81.1 -65.3 V86 1880.5 1348.5 -97.1 -118.6 V87 285.5 1438.1 539.6 -154.1 V88 592.0 1683.6 417.2 ~251.6 V89 1553.9 413.2 33.2 252.5 V90 483.5 943.2 460.5 42.2 V91 1625.0 1756.8 4.9 -280.6 V92 1091.9 942.3 217.7 42.5 V93 1836.7 1002.1 -79.5 18.8 V94 1672.9 958.8 -14.2 36.0 V95 1770.4 1222.9 -53.1 -68.7 V96 1978.3 1387.7 -136.1 -134.1 V97 1823.0 1099.0 -74.1 -19.6 V98 1346.7 557.4 116.0 195.3 V99 185.7 1175.1 579.4 -49.7 V100 1323.9 371.2 125.1 269.2 V101 1006.1 126.4 251.9 366.4 V102 1736.2 1215.1 -39.4 —65.6 V103 849.1 757.1 314.6 116.1 V104 1928.0 1901.9 -116.0 -338.2 37 in right ascension and declination from the cluster center (in arcsec). Finding charts for the variables are given in Figures B.1 - B.3 a,b,c,d, and e. 4.2 RR Lyrae stars The number of probable RRL stars in the NGC 6441 field has been increased from 11 to 40. The location of these stars within the CMD is shown in Figure 4.1. All previously known cluster RRL have been rediscovered. Only Layden et al.’s V36, a field star found west of NGC 6441, was not recovered, being outside the field of our observations due to our offset from the cluster center. Table 4.2 lists the mean properties of the individual RRL stars found in this survey. All periods were found using the phase dispersion minimization program in IRAF. Magnitude weighted, (B —— V), and luminosity weighted, (V), mean magnitudes were calculated using spline fits to the observations. Light curves for the variable stars are shown in Figure 4.2. Light curves were not shown for three of the suspected variables since no period could be found to fit the data. The accuracy of the periods found in our survey is i0.001d to :l:0.002d, depending on the scatter and completeness of the light curve. Photometry for the variables is listed in Tables A6 and A7 The periods determined for the known RRL are in good agreement with those found by Layden et al. As was noted by Layden et al., it can occasionally be difficult to distinguish RRc variables from eclipsing binary stars which have periods twice as long. This is particularly true for a cluster such as NGC 6441, in which a significant and variable reddening makes the precise location of a variable star in the color-magnitude diagram an uncertain guide as to the character of the variable. Although not always decisive, 38 j l . A. 16 — - A n— * —I A 00 C9 17 — — > __ A E] Ago ., _ Us 84; - - D (:9 _ 18 — - 1 I l l L l I I; l l l O 0.5 1 15 Figure 4.1. Color-magnitude diagram showing the location of the RRab (open circles) and RRc (open squares) in the field of NGC 6441. The triangles represent variables with uncertain classification. The field RRab star, V54, is is shown as a five-point star. 39 Table 4.2. NGC 6441: Mean Properties of RR Lyrae ID Period (V) (B -— V) Av AB Comments V37 0.614 17.541 0.862 1.17 1.55 V38 0.735 17.457 0.882 0.77 1.07 V39 0.833 17.669 0.995 0.70 0.95 V40 0.648 17.511 0.796 1.08 1.45 V41 0.749 16.720 1.222 0.41 0.75 V42 0.813 17.471 0.924 0.58 0.80 V43 0.773 17.524 0.914 0.60 0.80 V44 0.609 16.672 1.187 0.60 1.05 V45 0.503 17.374 0.836 0.87 1.07 V46 0.900 17.448 0.941 0.40 0.54 V49 0.335 16.762 0.727 V51 0.713 17.706 0.965 1.00 1.35 SV8 V52 0.858 17.458 0.966 0.23 0.33 V53 0.853 17.440 0.922 0.36 0.50 V54 0.620 16.531 0.952 0.51 0.67 Field V55 0.698 17.519 0.726 0.97 1.25 V56 0.905 16.495 1.143 0.64 V57 0.696 17.310 0.911 0.95 1.25 V58 0.685 16.864 0.865 0.70 V59 0.703 17.502 0.816 0.92 1.22 V60 0.857 16.820 1.137 0.29 V61 0.750 17.617 0.952 0.77 1.06 V62 0.680 16.884 1.146 0.51 1.02 V63 0.700 17.057 0.785 0.78 V64 0.718 16.982 1.343 0.95 V65 0.757 16.906 1.116 0.40 0.61 V66 0.860 17.054 1.262 0.44 V67 0.654 16.892 0.948 0.87 1.05 V68 0.324 16.130 0.608 0.49 SV1 V69 0.561 17.449 0.841 0.40 0.56 SV2 V70 0.317 17.503 0.640 0.20 0.70 SV4 V71 0.362 17.468 0.751 0.48 0.65 SV5 V72 0.312 17.344 0.665 0.48 0.65 V73 0.320 16.966 0.883 0.38 0.52 Field? V74 0.317 17.572 0.730 0.50 0.65 V75 0.405 17.345 0.710 0.46 V76 0.473 17.907 0.912 0.39 0.41 V77 0.376 17.488 0.708 0.47 0.65 V78 0.351 17.842 0.783 0.51 0.68 V79 0.417 17.223 0.916 0.68 V81 0.428 17.875 0.934 0.37 0.38 binary? V84 0.316 17.376 0.192 0.38 V93 0.339 17.331 0.765 0.54 V94 0.386 17.364 0.831 0.36 0.54 V95 0.090 17.603 0.686 0.55 0.67 V96 0.856 17.665 0.967 V97 0.844 17.441 0.975 V102 0.308 15.829 1.450 0.32 40 V37 P=O.614 V38 P=O.735 V39 P=O.833 I I f I I If I I I 17 1!. ‘. -1 17 __ J 17.4 1— IN 1“ --1 ll". -. “'1. 1 l. "o h"- 17.6 - l “1‘ l “'5‘ - V ”‘5 ' ”‘“~ . ”"1- J V 175 5‘1. l ””‘x, l ‘ V 17.8 1* l l 'i 18 ’— .~“'l.I: .Hu..-':-‘ No”... Q”... 18 1— |..." "'1]. + 175 l l 1 ‘r 1 1 1‘" 1 1‘. . V. V. d 1. I. I. I. 18 ’- . ‘1 ' .01 1 .' 1 .' 18 I. '. . '1 . . . 18.5 '- g k '- B . 1 ‘1, 3 ‘1. .1 B ' ”1, ‘1, 18.5 ~ 1 18.5 1- "“ ‘1', ~ 19 l .' 1' ' "'1‘ . ‘11 ._ '1". '1 I >- '.“1 '1'. "‘ 19 I 1 M1 1 ”'2 19 1 1 1 ' 1 L H 1 0 0.5 1 1.5 2 O 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase Phase V40 P=O.648 V41 P=O.749 V42 1320.813 1 l I 16.4 I H I I H 17 f 1 r 17 ,_ 's. W. -1 17.2 "' ."1 '1‘“ ‘ 1 ‘5-5 t l 111 I 1111‘ 1. . N. . Z 1 1 1 1, | f | 17.4 1 1 1. 1 V 17.5 - '11, ‘1: V 16.8 ”1111111. ”111111;; I V 17.5 _ "" 1' "" 1' q ‘5‘" I "~11.“ l I I. 11’ I. 11’ 18 '- \ '1 - 17 ,_ _, 17.8 - -< 175 1 1 1 1 1 1 1a 1 1 1 . 1“ 1" 17.5 "' [Ill|| I||||| ‘ 18 » ""1". ’0‘; B 18 '- l 1. l 1. '1 B , 1" , 1ll B 1'1". 1. H“. I' I]. 1‘. 18 10.x .1 .Mq 'I '1 185 - J. , ,I. . .4 18'5 In 1 "a. . H‘ “I “I ""11’ ""u' 19 ”’11 1 1 b 1 18.5 1 1 1 19 1 1 1 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase Phase V43 P=O.773 V44 P=O.609 V45 13:050.?) 17 I I I I I I I T WIT 17.2 - ', 3 iii ' N F 17 :1.‘ e'x,‘ 1 17.4 3‘. I ". " - b H‘ : :- u o \ .' \ . v 17.6 P- i“... I ‘kul I" "1 V 16.6 ”'1'. ' Ill.‘ I d v 17.5 1— "!u f 2‘“ I1 17.8 _ "ll '11. _1 16,8 '- Illu"" LIN"?! -1 ' I ' 'l 18 1 1 1 17 1 n 1 1 17.5 ., 1 1, 1 , 18 : 1H1. 1" 175 1- "... IN” ”3 I ‘3 I B185 ”'11. i ”'11. l B '1 ' '1 ' l B 18 I ‘1 ' ‘1 I , - ~ 18 1- n” , I" , _, ~ 1 '1 1 "9'"! '19....) NI".‘I ~"IQI’ 18.5 *- ‘o. . ~1I 1.. 19 l l 1 185 l l l 1 I l l I 0 0.5 1 1.5 2 0 0.5 1 1.5 2 0 0.5 1 1.5 2 Phase Phase Phase V46 P=O.900 V51 P=O.713 V52 P=O.858 I I 1 l7 1 I 1 17.3 r l I ."m ."m 1111 .1111 V 174 1.". "ll“ I" "II T V 17.5 " ”"1 ”"1 " V 174 —’ H'll ’ H’h d , .1 , .t. 1 IN”! | 'W'l' N "1 17.5 I I ‘1 175 .. l I I 1.. 1.. 11... 1 . ll 1 H I 18 “'5' "t, " "I ”Id 13 4. 1 1 "'1 1 “"1, ‘7-6 ' I 1 1 I 1 18.2 .. ‘1' '1'I ‘1' '1‘. .. , ”g , ”2 18.3 1’1’1'“ (”um - 1 . — '- '- ~ .. B184 .1 1“ 1 “‘q - B 85 . '1. . '1. B ‘5‘ 'I 1' l 1' ' ll“ ' '111 19 :1. ‘1-.. 1 18.5 I- l 1 1 i 18.6 l' |II '11 '1 i '0 '0 1' l '1 1' 1 Ill 11. 1 1 1 195 1 1 1 18-6 " 1 1 1 " 0 O 5 1 1 5 2 0 5 1 1 5 2 O 0.5 1 1.5 2 Phase Phase Phase Figure 4.2. Light curves for the NGC 6441 variables. 41 V53 P208555 173 '11 ' M15 '11 '11 17.4 11' 1 1’ 1 V 17.5 E111 1 i1'11 1 - 17.6 '1 .1 - 17.7 1 1 1 ‘ I I I 111 111 18.2 | '1 | '1 ~ 8 '1 1'11 " 1'1 18.4 I“ . I.“ ' I I 18.6 , .' .' J l I l 0 0.5 1 1 5 2 Phase V56 P=O.905 16.2 ' I 11 11 _ I 1 V 16.4 | 1 Hill”J 1 1 M“ 16.6 J I '11..“ ' I 1|...“ a 17.2 4 . P 1 .. I 17-4 L- 1"". 1"“: B 17.6 *1" 1' '1. 1' _ - I I J 118 mm! Wm! 18 1- 1 1 ‘ 0 0.5 1 1.5 2 Phase V59 P=O.703 I I I 17 1". ,'. -1 ".1 "'1 V175 ~'“fl ' W”. ‘ ”1"“ . I I11"“ 18 _ '11' 111'- 17.5 1. 1 1'. 1 I . I 18 *- ‘1, . .1. j 'N ' 'H ' 18.5 h ““11. 1' “hill ' 19 l 1|“ J L 1|“ 0 0.5 1 1 5 2 Phase V62 P=O.680 16.4 1 1 16.6 8 1]" 11" « V 16.8 '- I I I‘ " '11. ‘11. 17 HIM] “111'“ 11 17.2 - 1 I ~ 17.5 '- '~§‘ '15. .1 1 1 B 18 ~ ' " ' "1 u ' "111'. ' ‘“II 18.5 -11. 1 1 11' 1 “ o 0.5 1 1.5 2 Phase 16.2 16.4 16.6 16.8 17 17.2 B 17.4 17.6 17.8 16.7 V 16.8 169 17 17.7 17.8 817.9 18 18.1 16.6 16.8 V 17 17.2 17.4 17.5 18.5 V54 P=O.620 : '1 3“ '1' "3‘1 31.,“1' 8...“! _. '- 1. '1 1...! :1 - 1. 31 In...’ 11’ f 1 I..:111,‘.a"l ‘7‘ o 0.5 1 1.5 2 Phase V57 P=O.696 1." I 13' _ . ‘1. . "1. _ 1;. "'1 “dd 111' “.1 "1',“ _ . 1,. a". . :11- mM" “111': 0 of5 1 1‘5 2 Phase V60 P=O.857 '11 '11 )"111M1' 111 “ll. : 1 1 . MW“ “plum“; ['NIJI “I lll'fill I: o 0.5 1 1.5 2 Phase V63 P=O.7OO r ' ' ' - L"1H "1'1 ‘ -l I - 1' I'MI'IHIIW 1 A'HMIMW .1II'N‘H'1II' - +' I"“11I111L1' N "'1'11111 o 0.5 1 1.5 2 Phase V55 P=O.698 17 11" ' l ‘ I . V 175 L ”‘Ia " 1 - ' "111 1 1| 1 18 1. M151 MM. 17.5 -.. T '3. T - B 18 '- ‘N' ' ‘55 ... I 1 18.5 - l1111‘ 111. " 19 4 h. "I 1 I'm" 0 0.5 1 1 5 2 Phase V58 P=O.685 16 I I I. 16.5 - “£1111“ ”Juli" - '1 l 1 1 17 11"“1, 111111111111 "11” ' "11 l B .' ”'11 1‘11“ 18 11111 '1111111' "12 0 0.51.5 Phase V61 P=O.750 17 u 1 1 .0 '0‘ 175 3x ' ' — V “MINI 1 "Hull 1’ 18 - ' ' ' d 18 _ 1 ‘fl‘: 1 '11:; B 18.5 5|'11. \11. d 19 - "HM-.1 NH‘”. 1 -1 o 0.5 1 1 5 2 Phase V64 P=O.718 16.8- H II V 17 [111mm Inn” 111 “"111" Ml 1“ 17.2 I "I I1 18 _ 1 1:1 I 1:1.4 8 11‘ 1 ''11 1 "' 18.5 - I111111“ 11' “111111..I 1" ~ 19 l J l 0 0.5 1 1.5 2 Phase Figure 4.2 (cont’d). Light curves for the NGC 6441 variables. 42 V65 P=O.757 V 16.8L ' .U‘; T 'l'hi '11 "In ‘11! . ‘7 I”IIII' HIIIII' 17.2 "' l "‘ 17.6 1- ' .I1 ’ r -1 17.8 — B 181.... '1'” 3qu 18.2 ’ ~l"11"” "“qu ~ 18.4 ~ 1 , 1 ~ 0 0.5 1 1.5 2 Phase V49 P=O.3353 16.6 1 T r 1 1 v1 .8 1.. / '1' j, 1 17 .‘II ‘II - B 1 I. 1 h 17.6 1‘- 'f 1‘ 1' -I 17.8 '3‘"; 1 1k”) 1 " o 0.5 1 1.5 2 Phase V70 P=O.3166 17.2 r. . h 17.4 I. 1' '~. 1" 1 V I. 1 1. 1 17.6 - 1 | ~ 1 ' '1 178- '1! ‘01 . 18 "H 1.": 8 LL‘ 0" ‘1‘ 1' 1851 “HI Wv' o 0.5 1 1.5 2 Phase V73 P=O.3196 16.6 I I Y 16.8 1'". ”,qu‘ “,J1 V 17 " .Q‘ I '1‘ O " ‘1 1 ‘1 1 172 ~ 1' P' - 1761 ’T 11 r H 1.1 '~ 1 '~ -I B 171.: i 1 "-1 , d Mb1’ L 'I‘hl’ o 0.5 1 1.5 2 Phase Figure 4.2 (cont’d). 16.8 17.2 18 18.2 18.4 18.6 16 V162 16.4 16.4 16.6 B 16.8 17 17 17.2 V 17.4 17.6 18 18.5 17.4 V 17.6 17.8 18 18.2 18.4 18.6 V66 P=O.860 11111 11111 9'11“” 1- I I 1111': 1 “'11!” O 0.5 1 1.5 2 Phase V68 P=O.324O - :'"""IT 7"‘4-1 1 ' I1 |1 1.11 I-1..I 1 - “HI khl 1 ’ 1' "h 1" "'11 1.1 1 I11 I.‘ I I. 1 3.1.1.1 "1.1.11 - o 015 1 1:5 2 Phase V71 P=O.3620 '2'”. 1.”. 4 13- x ‘11 x —' _ II 1' II '1‘ 1"". 1 1"". .-I .-I :1 ”s ..-‘ "1 1 1. 1' x. t - “.u 1 ‘11., 1 q 0 0:5 1 115 2 Phase V74 P=O.3173 . HIM" "w“. a .- 1 h I "1 "11" "h" l" . '1'!" ' I"! 1‘ I l‘ t 1 X 1 \: LMI'I "Isml' " "1 o 0.5 1 1.5 Phase 43 V67 P=O.654 I ‘1 I V 16.5 “MI ”I!“ 17 "'~:|l'||' l| u"":ll'luil'-' ‘7 ‘ 1' r .'.1 ' '1 L B 17.5 “I" I "1" I 18 1- ll'III ml l"I11 111' q 18.5 I ' ‘ o 0.5 1 1.5 2 Phase V69 P=O.561O 17.2 1. I '11". fl f”; .. 17.4 b .1 1' 'I 1' _. V I I 1‘ 1! I I 17.6 45.11 "”134 ~ 18 - $1. I 11' d B 18.2 - ' ' 1 -1 18.4 r .111" I}. .IH' '1- 186 "M" I Lu" L ' o 0.5 1 1.5 2 Phase V72 P=O.3116 17 I fi fi 17.2 I 1’1""... I""'., . V 17.4 -, '1. '1' 17.6 I! ""1! "'3 17.6 - ' ' ' 4 17.8 - ,P'H. ,P'H. . B 13 - J 1. ,’ 1I a Iii :~' . . ‘~-: 0 0.5 1 1.5 2 Phase V75 P=O.4050 17.2 . .1 ' I~ . v 1" '1! I f" IiI I 17.4 - “1‘1. 11.1.1” In 111 17.6 . 1 1 1 ~ ”-3 ”|.I'- I.I'n ‘ B 181 '1‘. '1 i 18.4 1 1 L o 0.5 1 1.5 2 Phase Light curves for the NGC 6441 variables. V76 P=0.473 17.6 - I ' I 178 - Wk [a V - I "p" 'Ih “'1 1 18 "In; |.|' l.:' I“ 1 _ 182 — . _ 18.5 - ”fill 1 Fl": 8 18.8 I. II?“ II "*1! L 191% J 'k I 192 - 41 1 . q 0 0.5 1 1.5 2 Phase V79 P=O.417 16a . 17 - 1"” IIHI V 17'2 41W ”I“ "i" I” 114 17.. i II + Jflli + - 17.8 - 1‘ .“I - B ‘8 * .l' I. ‘1' 1‘. 18.2 r.- I, |'|' '11 18.4 >11 Ii ‘ 166 “I 1 LI” 1 0 0.5 1 1.5 2 Phase V94 P=O.386 17 1 ' 172 F pmfi "V*h V 114 . ’11 I‘d." 1].“: 17.6 I" I“ .. 118~ ‘ g 1 18 b I'M" 1|.Ill i B 18.2 h P" In. I. ‘m-I 164‘“; .h; 18.6 1 1 I 0 05 1 15 2 Phase V97 P=O.844 17.3 I V l - V17.4 II&MI HIMMfi 176 “I | "I l 176 I I l I _ 1&3 I h I ' W _ B 18.4 IIII III“ |"r 11,1 18.5 “I ' MI I 1&6 I 1 1 I 1 - 0 as 1 15 2 Phase Figure 4.2 (cont’d), V77 P=O.376 17 1 T 1 17.2 - “I.\ .1"\ _ V17A - " IR '5 ,3_ 116- .. M 118 I"'1!" , fiip’ 1 '1‘" .l‘" B 18 - 1f 1. 1‘ 'K— J I. 1 J I" 166 4, 19 q 0 0:5 1 1:5 2 Phase V84 P=o.316 17 ”'2 I1 WIIIIIIHU 1I HIM! 114 I 116 lfliql Ihflwfl 17.4 *- ‘ f‘ J B 1‘ I11) ‘ 17.6 i I "| 'H 173 JP“ . 'hfl . 0 as 15 2 Phase V95 P=0.090 17A . I ':V ' .24 J .I 1' - V 17.5 11““. r 11“". i. ”'8' '1' . 1': ~ 18 - H“. “a; B 1'. 1 I". . 1111...: 11......) 1 O 04.5 : 1f5 2 Phase V47 P=o.703 16.5 :‘I'I‘muL' "Inna-""3", If? V 17 . . + 115- % u : % h 17.5 :"W‘N‘; '".-"‘~ WW. I": B 18» - o 03" i {5" 2 Phase 44 V78 P=O.351 17.6 ; 'h‘.; in'lfi‘ 17.8 -1 f 1 f V 1a 3'1 r' "1 1' 11p 1.“ igg i 1 1 : . 1| II 18.4 I 1 . t1 B1&6£u " I1 ‘1 q 18'8 F 'l ,1' 0' “I .. 19 ' "'11 hmll .. 0 0.5 1 1.5 2 Phase V93 P=o.339 17 ' | I T ' _ “ II V 17.2 - III III“ I" ”W 114 | - a” 1 _ 116 II” 1 hi: ' 171:: 4'1”" “'13; 1 ,l I . 162 1 J l 1 4 18.4~<~IL 1“”. " o 0.5 1 1.5 2 Phase V96 P=O.856 17.6 I "MI!" I “MI!“ V117 WI I My , 11a . 18.5 - I‘ III 186 I 'IIII'II 'III'M 18.7 I'll ;v‘lll 18.8 _ 1.5 2 5Phase V48 P=O.668 15.4 1'“ "I." In“ I”... - V156 - . ~ , ' 1 4 15.6 _ i. l \J '1I I II.“ 15.7 - 1 P 1' : 163 f“ ’4' ”"1 3” q 816.4 '- I ‘ ' . 5 J 166 L I' h] I] hi 166 I. , 1l 0 05 1 15 2 Phase Light curves for the NGC 6441 variables. V50 P=O.433 18 - 11 ' 1|h.‘ 11 ' 11.1' 18.2 - '1'" " 1 4'! 1| .1 ,1 I 1 ,1 l 1 ‘ 18.4 1‘ 1| 1' 1| 18.6 - 1 1 1 19.2 - WI"! 1”" W!“ 1" 819.411. 1" I" '1" 19.6 19.8 W 1I J 15I 2 0.5 1 1. Phase V82 P=O.747 ‘5" 1111' 1111. r111. 1111' V‘fi'5 ' "'1’ 1 1 '"1‘‘ 11 16.6 - 11" 1"- 1 1 J 1 1 17.41”!“ ‘11'11 I1|1|ll “1'11 1 817.5 , H' 11 H' 1'1 17.6 1 ll 1 1 ll 0 0.5 1 1.5 2 Phase V86 P=O.325 17.8 M" '1‘! F1" II11 ' II '1 1' I. '1 I V 18 h '. I 1 ' '. | 1 '7 1' | 1' | 18.2 - 1 1 h 4 1 1 h -1 18.8 — 1 1 1 - 19 _1lll,1111'I'I 1'1I 1M. 1“ B 19.2- ' I“! 1 11 '1'1 . o 2 5Phase V89 P=O.456 18.3 I '8-4 r I! 1 1 11’! l V 13,5 J'I | ‘ ll" 11' I ‘ '11: 18.6 Pl ' 'h I ' Ifi -1 13°; ' 1 l ‘ 19:3 1111‘ 1,11 1111‘ 1' B ‘9" ”I H '1 1' 19.5 — I 19.6 P I 1 1 ‘I 1 7 o 0.5 1 1.5 2 Phase Figure 4.2 (cont’d). 17.2 17.4 17.6 18.2 B 18.4 18.6 17.5 17.6 17.7 17.8 18.5 B 18.6 18.7 - 18.8 17.1 17.2 18.2 B 18.3 18.4 18.4 18.5 18.6 18.7 18.8 19.4 B 19.6 19.8 V80 P=O.900 ‘ ”I." 1". ”J1“ 1 1-1 " 11 1 1 " 1 1 -1 F 111 1" 111 1'. _ r- If] I" .- o 0.5 1 1.5 2 Phase V83 P=O.622 1 '1'1 1'1 1'1" If jll II. I‘M“ ‘1 l #15:“ « ~11 1 1 1‘ 11 II.I 11K 11" M 1,1 111' 1,1 In" P,“ 1 1’“ 1 : 0 0.5 1 1.5 2 Phase V87 P=O.369 1" 1, f" _ a" ‘1 11' I!“ I. I1 1 II b '1' 1 '1 'P . '11 1 1'1 1 1'1 J'Iill "I'rI'M" Phase V90 P=O.726 “1‘! I" r1” "' ‘1 1”“ 1' '1 1' “'1 9 11 1 "1' 1' r. _ {1" I I l i.“ I v .. 'l ‘ “I'll 'l' i a “II b 11 ll' 1| IP 0 0&5 41 1f5 2 Phase 45 V81 P=O.856 17.3 1' :11'1'11" :11'1'11 V 17.9 4‘ '1 I11 1 - 1131? Z111 1 11111 : 113.7 '11'11' 11111] 1 1 812': E1 '| I“1'| - 1'9 _1 ' 1' _ 19'10 1‘ 015 1 II115 2 Phase V85 P=O.283 17.5 - 1 ' | ' 1 ' | 17.61 1‘11i I“! 1111' H V17] 1 1 1 n 1 - 11 1 11 n - 17.9 J ’ 1 1f 1+ .. 1|"! 1“ 818.8 "1"H ' 1 '11." ’511‘ 19 ' 11' 1'. 192 o 0.5 1 1.5 2 Phase V88 P=0.226 17.6 firmu". #111111". .1 V 17.8 -| "1, 1 '51“ 11 1' 18 - 1 1 1 111 1 111 18.8 - I‘ h“ 1* ”1" d B 1 1 1 19 1' 1 1 r 1 . U 1 I o as 1 L5 2 Phase V91 P=O.457 19.2 1' 1 I 19.41'11'1, .1'1. “1. 1 v::-: ' 1'1 "'1 .10 _ (1" 1 1 B 21 - I‘h‘l ”2'1“”: 21'50 0:5 1 115 2 Phase Light curves for the N GC 6441 variables. V92 P=O.577 1212 ' I..' ' I V 12': IIMIIIII I'll IIHIHIIII’MEW 18:8| I' II I' .. 8:6 I'l'irIIII'h'I II'I'IFIIIIM 19.8 A I _ O 0.5Phllse1.5 2 V102 P=O. 308 15.8 IIIM ”3:21.. WI! IWIIII': ELI. II I, I] 1313: "H". WWI: O 0.5 thlse 1.5 2 SV1O P=O.376 ,;;-:I I. II I I V1;’-71lillllvnII'IlIt) llillillvnIIIIII“ 89:5 It I W‘I II 2 Phase Figure 4.2 (cont’d). V100 P=1.656 .' ”‘3‘" AFT .- #5:." a n- 17 i" I" V 17.5 .' I' Fin“! 0.3a? o" :iLh-‘u 'a~ 18 H. 1' — B : 18.5 III II .. I Ii L o 0.5 1 15 2 Phase V103 P=O. 673 18.3 [I II “I V154 W II'II II III'III II' 'IIIIIII 18.6 'r I I II I| II 19.3 I I II I I 819.4 II Wm“ III WIII'H 19.5 I I I I 5 a 0.5 1 1.5 2 Phase SV11 P=O.474 17.65 - “I‘d Ill! h III V17.7 II III“: III I“ 17.75 — ”II 17.8 I: I 18.7 p I 'III| I III s m I N I ' I N I :I IIOI IIIISIIIII 13.9 o 2 5Phase 46 V101 P=3.500 18D ~r’flw'5, “I 3".“ I. 18.5 V 19 19.5 20 I . 20 '- I B 21L- 22 1 W- l o Phase V104 P=O.735 20.5 B "'I I "I 21.5 I VS: [ IIIIIIWI 17.6 17.65 '- 13.4w“ I IIfillII B r "WI!“ I "III!" Phase Light curves for the NGC 6441 variables. inspection of the Fourier decompositon parameters of the light curves can be an aid in classifying variables, and in distinguishing RRab from RRc variables. Fourier decompositions of the light curves were done using an equation of the form: may 2 A0 + Ajcos(jwt + (25,-) We then plot the Fourier parameters R21 vs. ml to give a clear distinction between RRL types (e.g. Clement & Shelton 1997), where R21 = 142/141) and (1521 = (1)2 — 2(151. Figure 4.3 shows a plot of R21 vs. (1521 for the probable RRL variables in the NGC 6441 field which have clean light curves. The values are listed in Table 4.3. A clear break between the RRL types can be seen at R21 of 0.3 as was originally shown by Simon & Teays (1982), with the RRc stars falling below this value and the RRab above. It should be noted that V49 falls in the same region as the other RRc variables, furthering the case for its reclassification (see Section 4.3) . The period-amplitude diagrams for this cluster in B and V are shown in Figure 4.4. There are a few RRab variables whose amplitudes are low for their periods. Some of these are probably attributable to noisy photometry (V46, V52, V53, and V55), while others are due to possible blending effects as discussed below. The Blazhko Effect can also reduce the amplitudes of RRab stars, but our observations do not extend over a long enough time interval to test for the presence of this effect. Another striking feature is the lack of a significant gap between the shortest period RRab and the longest period RRc. 47 ' l ' l ' l 0.6 - - © .. OO . C8 000 0.4 ~ 0 - F: O: 0.2 - - O O . CO 0 o O . O . I n I . l O 2 4 6 ¢21 Figure 4.3. A plot of the Fourier parameters R21 versus $21 for NGC 6441. The filled circle is the field star, V54. 48 Table 4.3. NGC 6441: Fourier Values ID 4521 R21 V37 V38 V39 V40 V42 V43 V49 V51 V54 V55 V57 V59 V61 V69 V70 V72 V73 V74 V77 V78 4.320 4.427 4.650 4.315 4.686 4.353 4.881 4.406 4.049 4.489 4.360 4.490 4.480 2.956 4.525 4.190 5.158 3.957 3.587 3.970 0.523 0.470 0.427 0.496 0.413 0.428 0.107 0.506 0.322 0.469 0.522 0.424 0.462 0.178 0.083 0.099 0.091 0.090 0.118 0.092 49 In I I I I I T I I . .. .. I _ 1— I. V B I Amp * [BEBE *.l ;. "" a D '- I] 0. DC] I I "" h ‘” *‘l-I '- 05 F El O I l l l l A l I -0.6 —0.4 —O.2 0 -O.6 -0.4 -O.2 0 log P log P Figure 4.4. Period-amplitude diagram for NGC 6441 showing the fundamental mode RRL (filled squares) and the first overtone RRL (open squares). The dots represent the “red” fundamental mode RRL. The asterisk, V45, and the star, V54, represent field RRab stars found in the field of N GO 6441. The mean level of the NGC 6441 HB determined from the probable RRL mem- bers, excluding the brighter and redder RRab, is V = 17.417 :t 0.298. 4.3 Notes on Individual RR Lyrae V45 - V45 appears to stand out from the other cluster variables. The shape of the light curve indicates that the variable is of ab type. Although our data present a gap in the light curve near minimum, we were able to determine a period similar to that in Layden et al., whose phase coverage is more complete. Layden and collaborators list the V amplitude of the star as 0.73 mag. We estimate the amplitude to be about 0.85 mag from our data. When we place this variable in the period-amplitude diagram for the cluster (Figure 4.4), it clearly stands apart from the variables we feel certain are cluster members. It is our belief that V45 is a field RRL that happens to fall at 50 nearly the same distance as the cluster. V49 - V49 was classified by Layden and collaborators as a possible detached binary with a period of 1.010d. Our data indicate that this variable may instead be classified as an RRc-type variable with a period one third as long. When the Layden et al. observations are fit to a 0.335d period, we get a light curve similar to our own, although with some scatter. V49 lies toward the outer parts of NGC 6441. The color of the star fits well with the other cluster RRc, but it is slightly brighter. We are unable to determine what, if any, reddening effects may contribute to the difference in brightness. At a period of 0.335d, our data for one night (~ 817.) nearly completes one cycle. Although we believe that V49 is more likely to be an RRc than a detached binary, more photometry of this star would be useful in making a definite determination. V52 - This variable has a period, magnitude, and color that would classify it as being an ab—type RRL. Yet, it is interesting to note that its light curve has a more sinusoidal shape. To illustrate the difference, it is good to compare the light curve of V52 with those of V46, whose period is slightly longer, and V53, whose period is similar to V52. Both V46 and V52 exhibit a sharp rise in light to maximum, where V52 has a more gentle slope. V54 - This variable is an RRab with a clean light curve. It is ~09 mag brighter than other cluster RRab variables. In addition, the distance of V54 relative to the cluster center indicates that it is a likely field variable. V64 — This star is blended with a close neighbor, only 1.3 arcsec away. The RR Lyrae-like periodicity shows up in the photometry of both stars, indicating that the 51 photometry of both is probably affected by the blending. The B light curves for each star have significant scatter with the amplitude of the star listed being 0.95 mag and the other being 0.60 mag. The V curves show a lot of scatter with amplitudes around 0.30 mag. The magnitudes for the other candidate are (V) = 16.97 and (B — V) = 1.4. V67 - This variable is found only ~35 arcsec east from a much brighter star. Therefore blending was a problem for some of the nights with poorer seeing. Although its color is similar to the other RRab stars believed to be on the NGC 6441 HB, it is slightly brighter. This may be a consequence of its proximity to the bright star. It should be noted, however that the ratio of B to V amplitude is not unusual. Its large distance away from the cluster center could indicate that V67 is a field star. V68 - (SV1, Layden et al.) We are still uncertain as to how to classify this variable. It appears as though the scatter in its light curve comes from blending with a close companion star. Also, coma may be affecting our photometry since V68 is found near the edge of the frame. V68 is unusually bright, and if it is found to be an RRc variable, it should be considered to be a member of the field. V69 - (SV2, Layden et al.) Even though it has an unusally long period, the light curve shape coupled with the location in the CMD indicates that V69 is a cluster RRL of c-type. (See Section 6.1) V70 - (SV3, Layden et al.) Our light curves for this star show that it is better classified as a binary rather than an RRC star. The location of this star in the CMD, which puts it in the vicinity of the RRab stars, also indicates that the star is not a c-type RRL. 52 V71 - (SV5, Layden et al.) The classification of this variable is still uncertain due to the scatter in the light curve. It does fall among the other cluster RRc in the CMD which gives a good indication that it is of this type. V73 - This variable has an uncertain classification. In the CMD, it is located slightly brighter and redder than other RRc variables. The light curve shape is somewhat asymmetric, but there is also scatter to indicate there might be some problem with blending. The distance of V73 from the cluster center is large enough to raise the possibility that it may be a field star. V75 - This star falls among the RRc stars in the NGC 6441 CMD, but there is some scatter in its light curve, especially in V, that makes its exact classification uncertain. V76 - This is a longer period c-type RRL with a light curve similar to that of V69. It appears to be fainter and redder as compared to other RRc stars on the HB, which may be an effect of differential reddening. V79 - V79 is an RRc star as indicated by its B light curve. The V light curve has a lot of scatter in it and the B — V color for this variable, which is somewhat redder than the other RRc stars, is uncertain for that reason. V81 - A probably binary star, but the phase coverage is not complete. V84 - This star appears to be of c-type. It is very blue as compared to the cluster RRc. There is a lot of scatter in the curves, especially in the V light curve. The mean B — V color is probably unreliable. V93 - The scatter found in the light curve of this variable makes it difficult to classify. It has a slightly asymmetric V light curve. The placement of V93 along 53 with the other RRC variables along the horizontal branch suggests that it is a RRC variable. V94 - This variable falls along the horizontal branch, although it is slightly redder than most of the RRC variables. The light curve shows an unusual shape having a longer than usual rise time. The precise classification of this variable is uncertain. V95 - From the shape of the curve, the location in the CMD, and its period, this star is a foreground 6 Scuti star. V96 - The somewhat asymmetric light curve and long period of this variable indicate that it could be an RRab variable. It is difficult to make an exact determi- nation of the variable type due to scatter found in the light curve and a gap present along the rise in the light curve. The location of this variable, slightly fainter and redder than other RRab variables, may be an effect of the differential reddening. V97 - The period found for this variable is similar to those found for other RRab variables of NGC 6441. The B data show definite variability at 0.844d, while the V data show only scatter. We have not given it a definitive classification since we see no clear minimum in the light curve. V102 - The classification of this star is uncertain. The B light curve looks to be that of a c-type RRL. V102 is much brighter and redder than the other c-type RRL found in N GO 6441. It is unclear whether this is due to blending or if it is a member of the field. The V light curve has more scatter in it than the B light curve, implying, as with the red RRab, that blending may be the cause of the difference, although, the shift in color of the RRab stars isn’t has great as that of V102. The V amplitude for this star, as is, would be at most ~ 0.1. 54 SV6, SV7, & SV9 — Two of these suspected variables, SV6 and SV7, from Layden et al. did not show any variation from our data. Layden and collaborators designate these stars as possible LPVs. Since our survey was not geared to search for LPVs, these stars may indeed be varying over a longer time scale than we sampled. SV9 was not in our field of view. 4.4 “Red” RR Lyrae It was noted by Layden et al. (1999) that V41 and V44 stood apart from the other cluster RRL in NGC 6441 in that they were both brighter and redder. With the increased number of RRL found in this survey, we also found an increased number of these unusual RRL. V62 and V65 are both brighter by approximately 0.65 mag and redder by approximately 0.25 mag in color than the other RRab stars in NGC 6441 which fall along the HB. Layden et al. put forward the hypothesis that these stars were variables that have unresolved red stars contaminating their photometry. This seems the most likely explanation. NGC 6441 has a very high central stellar density, indicating that crowding effects are highly likely. A consequence of blending with a red star would be an unusually high ratio of the B to V amplitude. This indeed seems to be the case for V41, V44, V62, and V65. Several other possible “red” RR Lyrae stars were noted, but they all had large scatter in their V light curves. It should also be noted that the V light curves of all of these variables tended to exhibit a higher scatter than the B light curves. If the unusual color of these stars is to be explained by unresolved companions, it is perhaps unexpected that all four such stars are of type 55 ab rather than including some of type c. On the other hand, it would be easier to discover blended variables with larger amplitude, all else being equal, which might favor blends involving RRab stars. 4.5 Reddening Sturch (1966) found that near minimum light the blanketing-corrected and reddening- corrected color of RRab stars were a function only of period. The observed color during this phase could therefore be used in determining the reddening of a RRab star. Blanco (1992) modified Sturch’s procedure by incorporating the metallicity indicator, AS, where AS is the difference in spectral type based on the strength of the Balmer lines and the calcium K -line near minimum light for RRab stars. He found E(B — V) = (B — V)¢(0,5_0,8, + 0.0122AS — 0.0045(AS)2 — 0.185P — 0.356 To infer AS for the NGC 6441 variables, we used two different methods. The calibration of Blanco (1992) which makes use of high resolution spectra of RR Lyrae stars gives: [Fe/H] = —0.02(j:0.34) — O.18(3c0.05)AS Suntzeff et al. (1991) based their calibration upon the globular cluster metallicity scale adopted by Zinn and West(1984). They found: 56 [Fe/H] = —O.408 — 0.158AS Taking the value of [Fe/H] = —0.53 (Armandroff & Zinn 1988) and calculating the AS value we find that the Suntzeff et al. calibration gives colors which are ~ 0.02 less red than that given using the Blanco calibration. Table 4.4 gives our reddening determinations for RRab variables with good light curves using the Blanco calibration. Some variables had not yet achieved minimum light in the 0.5-0.8 phase range after maximum light. The points in this range were averaged to find (B — V) in all cases. The reddenings found in this way for the stars labeled as ”bright and red” may be incorrect, since those stars may in fact be unresolved blended images, as noted above. The mean reddening value for the remaining 10 RRab stars which are believed to be probable members of NGC 6441 is E (B — V) = 0.53 i002. The range in reddening values (~ 0.1) is consistent with previous determinations (see Layden et al. 1999) that the NGC 6441 field is subject to significant differential reddening. Also shown in Table 4.4 is a comparison to the reddening values found by Layden et al. We see that our reddening determinations are somewhat higher than those found by Layden et al. The mean reddening value determined from the six normal RRab stars observed by Layden et al. is E (B — V) = 0.45 :l: 0.02. It is uncertain to what extent this difference arises from the discrepancy in the V magnitudes between our data and theirs since we have no way to compare with their I data. One should note that the ab-type RRL in NGC 6441 by their very nature are 57 Table 4.4. NGC 6441: Reddening Determinations E(B-V) ID Pritzl et al. Layden et al. Comments V37 V38 V39 V40 V41 V42 V43 V44 V51 V54 V57 V59 V61 V62 0.547 0.504 0.589 0.458 0.841 0.502 0.527 0.864 0.619 0.571 0.584 0.448 0.555 0.859 0.410 0.412 0.548 0.468 0.683 0.444 0.413 0.676 Bright & Red Bright & Red Field Bright & Red 58 different from those which Blanco used in establishing his relationship between metal- licity, period, and intrinsic color. We have assumed here that his formula is applicable to the RRab stars in NGC 6441. This might not be the case. Bono et a1. (1997) have argued on theoretical grounds that the red edge to the instability strip might lie at cooler effective temperatures for metal-rich compared to metal-poor RRLS of equal luminosity. If so, and if, as argued in this paper, the RRab stars in NGC 6441 are unusually bright for their metallicity, then Blanco’s reddening calibration might not apply perfectly, or at all, to the RRab stars in NGC 6441. Hesser & Hartwick (1976) determined the reddening of NGC 6441 to be E(B — V) = 0.46i0.15, while Zinn (1980) and Reed et al. (1988) obtained E(B—V) = 0.47 and 0.49, respectively, from their analysis of the integrated cluster light. 4.6 Eclipsing Binaries and LPVs We were able to find a number of eclipsing binary stars within our field of view. The binaries listed by Layden and collaborators were all recovered. Table 4.5 lists photometric data for the binary stars. Due to our sampling it was somewhat difficult to determine accurate periods for detached binaries. Our observations were not geared toward locating long period variables (LPVS), but we were able to detect some stars exhibiting luminosity changes over our 10 day run. These stars and their locations are listed in Table 4.1. We were able to reidentify a small number of LPVS already found by Layden et al. along with a couple of new LPVs. 59 Table 4.5. N GC 6441: Mean Properties of Binary Stars ID Period (V) (B — V) Av A 3 Comments V47 0.703 16.485 0.997 1.20 1.10 detached V48 0.668 15.497 0.889 0.31 0.32 contact V50 0.433 18.179 1.161 0.52 0.60 contact V80 0.900 17.404 0.989 0.38 0.40 contact V82 0.747 16.498 0.937 0.24 0.25 contact V83 0.622 17.620 0.971 0.28 0.25 contact V85 0.283 17.633 1.262 0.36 0.41 contact V86 0.325 17.942 1.111 0.48 0.50 contact V87 0.369 17.135 1.140 0.24 0.26 contact V88 0.452 17.694 1.142 0.44 0.46 contact V89 0.456 18.483 0.860 0.34 0.34 contact V90 0.726 18.519 0.997 0.30 0.34 contact V91 0.457 19.517 1.123 0.70 0.70 contact V92 0.577 18.578 0.967 0.34 0.39 contact V100 1.66 16.965 0.866 1.05 1.15 detached V101 3.50 18.318 1.226 1.75 1.80 detached V103 0.673 18.410 0.955 0.23 0.25 contact V104 0.735 19.404 1.264 1.05 1.15 contact 60 Table 4.6. NGC 6441: Mean Properties of Suspected Variables ID Period (V) (B—V) Av AB Aa A6 SV10 0.376 17.658 1.053 0.10 0.11 -294 169.8 svn 0.474 17.703 1.075 0.14 0.15 388.5 206.0 SV12 0.860 17.569 0.886 .. .. -111 -72.8 SV13 0.17 0.17 136.9 323.5 SV14 0.30 0.46 -28.7 -213 SV15 0.40 0.40 -26.4 -09 4.7 Suspected Variable Stars Following the naming scheme by Layden et al. (1999), we list in Table 4.6 stars which exhibit variability, but were difficult to classify for reasons such as high scatter in the light curves or abnormally low amplitudes. SV10, SV11, and SV12 all show some shape to their light curves which may indicate their variable type, either binary stars or RRL stars (Figure 4.2). Yet, the scatter in the curves matched with their low amplitudes, ranging from 0.10 to 0.15 mag in B and V, make them difficult to classify. SV13 appears to vary in magnitude over a period of days yet the amplitude found is only 0.15 mag. The photometry of both SV14 and SV15 Show that the magnitudes of the stars have a range in amplitude of about 0.4 mag. Again, scatter in the curves makes the classification of these stars unknown. 61 Chapter 5 VARIABLE STARS IN NGC 6388 5.1 Discovery of New Variable Stars All variables were found using the same two methods as used for NGC 6441 (see Section 4.1). The purpose of this survey was to detect short period variables. As a result, very few of the known long period variables were recovered. With the exception of saturated stars or limits due to field of view, all of the probable short period variable stars previously known were recovered during our variable star search. In addition, 29 probable new variable stars were detected. For the purpose of detecting and identifying variable stars, the B photometry was more useful than the V. As mentioned before, this was probably due to less interference from bright red giant stars. Finding information for the new variable stars is given in Table 5.1, where X ,Y are the coordinates of the variables on the CCD (the cluster is assumed to be at (1070,1068)) and Aa,A6 are the right ascension and declination from the cluster center. The finding charts for NGC 6388 variables can be found in Figures B.4 - B.6 a,b,and c, where north is down and east is left. 62 Table 5.1. NGC 6388: Locations of Discovered Variable Stars ID X Y A0 A6 V4 1560.0 999.9 -194.0 26.0 V12 1228.2 1067.0 -61.1 -0.9 V14 1532.5 1858.0 -183.0 -317.8 V16 1743.4 447.1 —267.5 247.4 V17 1170.8 1129.4 -38.1 -25.9 V18 1147.5 949.0 ~28.7 46.4 V20 938.0 965.0 55.2 39.9 V21 911.2 722.6 65.9 137.1 V22 901.0 1076.3 70.0 -4.6 V23 1528.6 1016.9 -181.4 19.2 V26 793.3 1228.3 113.2 -65.5 V27 923.4 1106.7 61.0 -16.8 V28 1014.8 1194.5 24.4 -52.0 V30 951.3 1089.8 49.8 -10.0 V31 768.4 823.1 123.1 96.8 V32 1170.9 1138.8 -38.1 -29.7 V33 907.3 854.0 67.5 84.4 V34 1562.0 1184.7 -194.8 -48.1 V35 898.0 535.9 71.2 211.9 V36 1004.7 1025.3 28.5 15.8 V37 1072.7 1127.3 1.2 -25.1 V38 1124.4 1052.1 -19.5 5.1 V39 1088.9 1638.4 -5.3 -229.8 V40 815.2 9.6 104.4 422.7 V41 904.7 525.6 68.5 216.0 V42 62.1 332.7 406.1 293.3 V43 456.0 620.1 248.3 178.1 V44 1467.1 1010.7 —156.8 21.7 V45 1607.4 1151.7 -213.0 -34.8 V46 649.7 341.7 170.7 289.7 V47 1283.6 1158.4 -83.3 -37.5 V48 359.0 1523.1 287.1 -183.6 V49 1004.9 1030.6 28.4 13.7 V50 1048.9 1168.0 10.8 -41.4 V51 1130.1 1006.1 -2l.8 23.5 V52 1006.9 1134.3 27.6 -27.9 V53 1530.4 1564.3 -182.1 -200.1 V54 1278.0 973.1 -81.0 36.7 V55 1589.2 1115.1 ~205.7 -20.2 V56 1037.2 1229.8 15.5 -66.1 V57 1130.4 1097.4 -21.9 -13.1 V58 1821.4 571.7 -298.7 197.5 63 5.2 RR Lyrae stars The variable stars in NGC 6388 have been studied previously by Hazen & Hesser (1986) and Silbermann et al. (1994). In the field of NGC 6388, the number of probable RRL stars has been increased from 11 to 15. Figure 5.1 shows the position of these stars within the CMD of NGC 6388. Of the previously known cluster RRL, only the bright RRL, V29, which is believed to be saturated'on our images, and V24, which lies outside our field of view, were not rediscovered. The mean properties of the individual RRL stars, and the one 6 Scuti star, found in this survey for NGC 6388, are listed in Table 5.2. The periods determined for the known RRL, using the phase dispersion minimization program in IRAF, are found to be in good agreement with those found by Hazen & Hesser (1986) and Silbermann et al. (1994). Spline fits were used to determine the magnitude weighted and luminosity weighted mean magnitudes for (B — V) and (V), respectively. Figure 5.2 shows the light curves for the individual variable stars. As noted with NGC 6441, the accuracy of the periods found in our survey are i0.001d to i0.002d, depending on the scatter and completeness of the light curve. Tables A8 and A9 lists the photometry for the individual variable stars. Due to the variable reddening across NGC 6388, we find, as before with NGC 6441, that the distinction between RRc variables and eclipsing binaries can be difficult to determine. Again, the Fourier decompostion parameters, R21 and 0521 are used to aid in distinguishing the variable types. Figure 5.3 shows a plot of R21 vs. 0521 for the probable RRL variables in the field of NGC 6388. Only stars with clean light curves were used. Table 5.3 lists the values of the Fourier parameters. As before, we 64 I E I 15- -1 16 — 3 > 1 . . A D 0A . . 13 AngO . [ID A A 17 - [DD 0 - . III . l- . 18 - * - ' 1 . 1 1 . . . l . . . . ' 0.5 15 B-V Figure 5.1. Color-magnitude diagram showing the location of the RRab (open circles), RRc (open squares), 6 Scuti (closed star), and Type II Cepheid (open stars) stars in the field of NGC 6388. The triangles represent variables with uncertain classification. 65 Table 5.2. NGC 6388: Mean Properties of RR Lyrae ID Period (V) (B — V) AV A 3 Comments V16 0.251 16.870 0.561 0.26 0.31 V17 0.611 16.502 0.708 0.85 1.15 V20 0.467 16.764 0.474 0.36 0.46 V21 0.813 17.004 0.780 0.87 1.15 V22 0.587 16.833 0.728 1.12 1.57 V23 0.337 16.869 0.544 0.48 0.65 V26 0.239 17.380 0.546 0.38 0.51 V27 0.365 16.931 0.603 0.46 0.67 V28 0.840 16.795 0.846 0.80 1.05 V30 0.939 16.756 0.892 0.80 1.05 V31 0.341 17.007 0.573 0.52 0.70 V32 0.524 16.553 0.632 0.42 0.52 S1 V33 0.558 16.723 0.731 0.29 0.42 V34 0.236 17.386 0.568 0.36 0.50 V35 0.299 17.014 0.552 0.18 0.23 V45 0.080 18.058 0.560 0.50 0.67 6 Scuti V49 0.355 16.541 0.455 0.34 V50 0.384 16.900 0.659 0.52 0.65 S2 V51 0.366 16.869 0.976 0.54 V52 0.397 16.580 0.737 0.34 0.48 V53 0.386 16.687 0.667 0.32 0.55 V54 0.333 16.829 0.786 S3 V56 0.489 16.771 0.669 V57 1.242 16.795 0.7214 alt P205506 66 V16 P=O.251 .7 I I I 16 .01 .I"|1 16.8 1— , N ’ K; v 16.9 '- "l I. ‘1' 1 17 JIM 1 JIM P .l 17.3 - full {1111 q B 17.4 " .1 ‘l " 17.5 H .' h. .' J 17.6 PM"! 1.0" , - o 0.5 1 1.5 2 Phase V21 P=O.813 ‘55 .. . .m. . 1 I.“ o I'.‘ I V 17 l- 7 . ! ‘.. I-1 17.5 - 1 Hf: 1 L "l: 7 I ' J. r o 17.5 h. 0. I. . I." B 18 _ ""1. f ‘ I I- ..io' ’0’ 18.5 1 ' 1 1 I - o 0.5 1 1.5 2 Phase V26 P=O.239 17.2 ~ Ir '1' ~ I’M ”I I'm "II V 17.4 ~ 3 I 1., I 1., 17.6 "'1 "J " .111 17.8 - :l'i‘ II 18.2' I 5'1. 1 ‘I o 0.5 1 1.5 2 Phase V30 P=O.939 16.6 '1' IT T |I ; 7 1' I III I v . ml 1 ml; 17 . '.' 1 J 17.4 I“. r I)". r - l I I I B 17.6 I“ | r 1" I - 1 H 17.8 I mum L mum o 0.5 1 1.5 2 Phase V17 P=O.611 16 __ I I r q “I, “I, V 16-5 IIII J'III hm l hm l .111 m .111 16.5 . ‘ ll ' ' - I IIII I I 17 ~ 8 111 I'111 17.5 - Ml)", L ""1”! -l o 0.5 1 1.5 2 Phase V22 P=O.587 16.5 - l‘,‘ K, 9 V I H. I H. 17 r, 5““! "I“: 165 "I % % MI % 17 l II. it. . B 17.5 - l "11.I ,1 ‘ a1, a ‘8 I“.-. . “‘1'“.-. 1 S“ o 0.5 I 1.5 2 Phase V27 P=O.365 16.8 3‘1" 'plh‘l‘. “11 v _ I .' I. .' - 17 ‘II II ‘11 ll 17.2 '7 {H I ("I “ 17.2 ~ )1 I 1);, . 817.4 '- ‘IH "I‘I .1" l’l‘ 11 17.6 P )1 1'; l1 1.; 17.8 bn'“ 1 |“1'IIII' 1 9‘ o 0.5 I 1.5 2 Phase V31 P=O.341 16.8 11ft I In“. r 7 I .I I I _ l I l l- V 17 '1 I. H I' 17.2 "' i"... II.“ 17.2 i i i ~ 174 T" I'M" I B ' II II II a 17.6 - 1‘ I~k -l 17.8 1- |II 1' 'I 1' " '1'". ”I'll 18 I L o 0.5 1 1.5 2 Phase Figure 5.2. Light curves for the NGC 6388 variables. 67 V20 P=O.467 16.6 I ”ll 1 I 16.7 ll I.II ll I' ~ V 168 9.11 rLl 1", LI .. 16.9 - 5,1,1? 1 M'l' 1d, . 13 — ' Ir ' H .72 ‘1 " ‘1 ' . - I .. 8 III "I“ 11 "HI 17.4 I'll" l '“Ifl ‘ o 0.5 I 1.5 2 Phase V23 P=O.337 16.6 ff]. f .141. f I V 16.8 ~ "( I" "1,, 1'1 1— ‘ ‘ -I 17 "fun! "1511' 17 II : lh : 17.2 J. .3 '1, .6 B ‘7" ” h“. I. ". I. ‘ 17.6l- 1.,“ . I...‘ . . I If I I 'f o 0.5 I 1.5 2 Phase V28 P=O.84O 16.4 I .1“ I 101.. 16.6 ~ I .. I .- V 16.8 r“ r "'1. r '4 17 r I N I .1 17.2 -H‘lul, . Ml ~ 17 ._ I p I I u .1 I '. I '. B 17.5 1;". : “Ly". .5 I?1 ‘3 ‘ "W. . "ll-(I1 “ o 0.5 1 1.5 2 Phase V32 P=O.524 ,l ' l ,‘1 ' 16.4 - I. ,I 1.. . V I I 16.6 {WIIIII' “Mull“ 16.8 " l 1 I " 16.8 ”11': 1 ' “l: ' B 17—' 'I5 . l‘ J 17.2 I "H '1‘ 1,5 ,1 17.4 I'll-Ir , ,‘IIIII— o 0.5 1 1.5 2 Phase V35 P=O.299 V33 P=O.558 16.6 {III I lull: - V 16.7 - 16.8 LI 'Il'HI (“I I) IN!" 16.9 1 17.2 r 111 111 « 817.‘ ’1’ ‘11. III' I“. -1 I 17.6 - law“. 1111"}! o 0.5 I 1.5 2 Phase V18 P=2.85 15.2 - I T # « 1... . I‘m III ,1 v 15.6 I '1‘ II 15.8 - « 16 - J. . III. - 16 ,__'T\ I I\ _, B 16.5 E “ '1 17 I. J1 l V'I ‘ o 0.5 1 1.5 2 Phase V38 P=4.878 V 15.5 - .1“ I I '1" I - B 16 :‘I'I .‘I I 1 16.501:\I1I‘1\I" o I 5 2 5Phase V40 P=0.536 .7...) ,m ,1 .m , V ‘3 ”III I lml III I lIlllh 18.1 I' ' "I 18.2 - II' . % I'I . « :2: P“ IIII .11" III‘ '1 B18.8 4'1 l M I) l )I'l- 185 f w . (:1 . I90 0.5 1 1.5 2 Phase Figure 5.2 (cont’d). V34 P=O.236 172 P I,“ ' I,“ 4 17.3 ~ III I5. ’II III: V 17.4 - ' '1 176- H H II- 17.8 - “1‘41qu U‘I'Il' B 18 - I'I. {I I’I 18.2 3'1"; 1 III'III 1 -‘ o 05 1 15 2 Phase V36 P=3.15 15 ax . AH V 155 - h \ . 16 a! : :0: i j 15 _ N ”N - B 165 r \ \ - ‘7 KI . .\I . ‘ o 05 I 15 2 Phase V14 P=2.16 16 ' ‘31 as, :T. “\y‘ 0‘ ,I V 16.5 L ‘.I "I9 17- I I« M 'ng I” "5" "II.’ 17 .. i I « B 175 p 1 o 05 I 15 2 Phase V41 P=0.311 185 - I I I .' 1". I. in! V18abehufi h [IIIH' .9 I '1 I' 19.2 1‘ 19.8 4|) ‘ulh‘I 'M'I Ann” IMF 8 20 “II 1.1 HI I 202 l o 05 15 2 Phase 159 W‘ M' V 17 1"")! IIIIII'III Ill IIIIIII'h‘ 171wa'IIF 174 I; 'PI 1751')” 'IIIIIIIIII) - 8175J 1 III “Ml P IIII‘L 177 L “(I IILZ o 05 15 Phase V37 P=10 I... _ ll ll 1 V147 ~' I I P 14.8 L I ‘l 14.9 '- l l l 1 'I f I I I 155 - II" II IF B 16L. '. 4 16.2 I 1 I p 1 o as I 15 2 Phase V39 P=O.412 ‘. T I “I W 18.2 II fl ’1’”. {I q I’III " V18.4 - I 'l lg '1 l I i3? II fig 1 I 194 g H III IIII'4I31 195 - (1 g 19.8 I- I II I I. o as I 15 2 Phase V42 P=1.71 ‘7 u;::v— I.——:::7 175 ~ . - 13 L ' - V185 l 'I - 19L 9 . 18 Tw- --I—r-- T.|-- --Lv-~ -l B 19 r u. r1 20» ° 5 21 l '1 l o 05 1 15 2 Phase Light curves for the N GC 6388 variables. 68 V43 P=1.82 F 14”" Qf 15.8 " | I ”55“.," c1 166 A ' 1 2' ' I”, ”D 8“". .ap 16.8 ~ '. " 17 I. I I -I 17.2 1 I l 1 I O 0.5 1 1.5 2 Phase V58 P=O.324 18.8 19 ”I"? .JI I’IIII'IH‘I'III IJI'F 19.2 *I ' III-‘1 19.4 f ..,' 19.5 r # 1 1 1 20 "JH‘ “I (“I4 I ‘hll‘ 8 Il IIMII II‘II 20.5 1' I I.'I1I| I.I l 0 0.5 1 1.5 2 Phase V50 P=O.384 16.5 - II.“ T 'lgi'h v16.8 " ”h" I" :1. '“T I771" III"I,I|I III"; 17.2 "H" 1 I“ 1 "‘ 17.2 LI"! I j," " 3132’ I" '1 1'" ' ‘ ' I. '1 I l-I 17.8 1.11 "1.1m" "'1 18 4 I O 0.5 1 1.5 2 Phase V53 P=O.386 16.4 I | I I I I I V 16.6 In!" ”1""1' ,I 16.8 " "mm” "mllfllh -1 I; 1" 1" 17.2 EIIII' ‘a’FIIJaII ”.1 17.4 '- Il'l ' 17.6 1 "1:11." III!"I!I . O 0.5 1 1 as 2 Phase Figure 5.2 (cant’d). V44 P=2.02 19.5 .. I" F 1" F \/ 20. - 20.5 — 1 1 « 20.51111“ 1"" B 21 - ' ' « 21.5 - « 22 1 l l a 0.5 1 1.5 2 Phase V45 P=0.080 17.8 p"! I I .'1 I . 11 11 V "8 .9 I“. ’ 1| I. 18.2 F- I'M“! IIIW‘ 18.2 ".1: " l .1 - 18.4 -'I I. 'I I. .. E318.6 : I'I' . 1"“ . 18.8 '- 1"."! l "I‘fI o 0.5 1 1.5 2 Phase V51 P=O.366 16.6 - III" III" - V 16.8 i- ‘M x": |H “if ‘7 ”I I' ""11" 17.2 -“ 1 | ”1 _ I'II rIIII 19o - 1.5 2 5Phase V56 P=O.489 1:: ~ 1 i' V I _ I "\ Ill "\ 16.8 - I I 16.9 I MI" “I 17 1 I 1 17.2 ~ III III" 17.4 hi I I B I'I 1‘ I (I I,“ "-61 . 11.11 . II o 0.5 1.5 2 Phase 69 V55 P=O.366 19 1': v13331II11"'1.1I"11"'1.1" 19.6 - | I || I 4 19.8 pawl“. ""11“ I" « 20 L 20 II 1" ' 1"I 00.515 2 Phase V49 P=O.355 16.4 - I'IIIII I I II V16.61HIIII ""11 W IIIIIII IIIIIIIE 16.8 . 15.8 .. 'p:l|'l I 'PIIIIII .. B . ' ' - ”I: WI "I'IIlfIII . "WU o 0.5 1.5 2 Phase V52 P=O.396 16.4 “'1‘" “I” M - V16.6 {I .3111“. III 17.2 - "II III - III B17A 1 "IHMIIIII In“; 1161; 0.5 1.5 2 Phase V57 P=1.242 16.6 Fl'll" II III." Il V 16.8 IIIIIIIIIIIII 'J’IIllIIIIIuHII SJ 17 ~ I I 1 . I‘lIl- 131i 3'11 . ”"1... I B J ' I 1;: _ III'III'fI "I'I'IE 18 ' 1 . o 0.5 1 1.5 2 Light curves for the NGC 6388 variables. Table 5.3. NGC 6388: Fourier Values ID (1921 R21 V16 V17 V21 V22 V23 V26 V27 V28 V31 V32 V33 V34 4.630 4.294 4.576 4.299 3.839 4.598 4.847 4.584 3.977 3.213 3.197 4.274 0.104 0.586 0.449 0.542 0.096 0.132 0.072 0.401 0.099 0.265 0.212 0.120 see a clear break between the RRab and RRC types at R21 2 0.3. Shown in Figure 5.4 are the period-amplitude diagrams for NGC 6388 given in B and V. There is one RRab variable, V17, whose amplitude appears to be low for its period. This may be due to blending effects. However, this variable does not show the shift toward redward colors as do certain RRab stars in NGC 6441 (Section 4.4). It should be noted that the Blazhko Effect can also reduce the amplitudes of RRab stars, but our observations do not extend over a long enough time interval to test this effect. As with NGC 6441, we see that NGC 6388 lacks a significant gap between the shortest period RRab and the longest period RRC. The mean level of the NGC 6388 HB determined from the probable RRL mem- bers is V = 16.892 i 0.239. 70 . I . , . I 0.6 - O O o 0.4 - 0 F: a: o 0.2 _ O O o .- OO O o 0 1 l 1 I n l O 2 4 6 Figure 5.3. Plot of the Fourier parameters R21 versus (1521 for NGC 6388. 71 1.5 I Amp I i O l l I l l l l l -O.6 —O.4 —O.2 O -O.6 -0.4 —O.2 0 log P log P Figure 5.4. Period-amplitude diagram for N GC 6388 showing the fundamental mode RRL (filled squares) and the first overtone RRL (Open squares). 5.3 Notes on Individual RR Lyrae V 17 - The amplitude is low compared to the other fundamental mode RRL. The ratio of the amplitudes is not unusual. There is some scatter in the curve indicating a possibility of blending. Its mean magnitude is somewhat brighter than the other fundamental mode RRL. V20 - There is a lot of scatter in the curve making classification uncertain. It falls among the other cluster first overtone RRL in the CMD. A bump may be seen at about 0.25 before minimum light in phase. V30 - This star fits in the CMD with the other fundamental mode RRL. The best fit to the data is a period around 0.939d. There is a gap in the data near maximum light through the decending light. This, along with scatter in the curve, makes finding the best period difficult. 72 V32 - (Sl, Silbermann et al.) A long period RRC type variable with some scatter in the curve. V35 - One night of observations of this variable (night 4) falls at a different phase and amplitude as compared to the other nights, as shown in Figure 5.5. Taking that night out, the data fit the period of 0.298d. V18 and V36 - Cepheid variables. The light curves in V tend to have more scatter due to reaching the saturation limit of the CCD. Crowding in the cluster is also likely to contribute to the scatter found in the light curves since both stars are found near the center of the cluster. V37 - A probable Cepheid variable. The maximum period fit to the data is 10 days due to the length of the observing run. Figure 5.6 shows in a plot of magnitude versus heliocentric julian dates that the actual period should be not much longer than the one given. The magnitudes are descending up to 5 days before maximum light is reached. V38 - Cepheid variable. No V data were available due to saturation. For this reason, the B data was placed on the standard system using a zero-point shift of +3825. From this zero-point shift, V38 seems to be oddly brighter than the V18 and V36. The reason for this difference is uncertain, although crowding may be an effect. V45 - From the shape of the curve, location in the CMD, and the period, this star is of 6 Scuti type. V49 - Shows definite variability, but has a lot of scatter in the curve making Classification difficult and the magnitude and color unreliable. The B light curve does show hints of looking like a c-type RRL, but the V curve does not. The mean 73 I I I I I I 0? LO ._ __ > t _ o 0 an. ' o 2 Nights 1—3 "‘7 Night 4 l I l l I I I I I I I I 0’. LO _ O O —r— > I\ _ . o . o____ o . o . I\ Night 5 ' ' “ Night 6 - l l l l l l T l l l l l 0‘. LO _ o o ‘h‘ . > ’\ — . O . O ‘_ . [1' _ Night 7 ' ' ‘f Night 8 ' I I I I ' I I O O 5 1.5 O 0.5 1.5 Phase Phose Figure 5.5. Nightly light curves for V35. 74 15.8 I l 16 l I 960 965 HJD 16.2 Figure 5.6. A plot of the magnitudes for V37 versus the heliocentric Julian dates for the observations. 75 magnitude of the variable places it along the HB, although slightly bluer than the other RRc. V50 - (SZ, Silbermann et al.) A lot of scatter in the curve makes the exact classification uncertain, although, the B curve looks somewhat like that of a c-type RRL. Its mean magnitude and color place it among the other probable cluster RRC. V51 - The light curves show scatter in them, especially in B, making classification uncertain and the mean magnitude and color unreliable. The V curve looks to be RRC type. V52 - This star shows definite variability, but a large amount of scatter exists. Its magnitude and color, although somewhat unreliable, place the variable among the other probable N GO 6388 RRL. V53 - A variable that falls among the first overtone RRL in the CMD of NGC 6388. An unusual light curve shape, which shows a sharp decrease in magnitude after maximum, makes its classification uncertain. This variable is found next to a much brighter star, which may be affecting the photometry of this variable. V54 - (S3, Silbermann et al.) This stars shows definite variability, but we were only able to observe it when the star was increasing in brightness. Therefore, the magnitude and color given for this variable are not reliable. V56 - A likely c-type RRL. The variable falls among the other probable RRC of NGC 6388. A gap occurs during the rising light in the light curve up to near maximum light, making the exact calssification uncertain. V57 - The data for this variable fit at two periods, 0.551d and 1.242d. The fit at P = 1.24d seems to fit the best, making it unlikely to be an RR Lyrae. Still, scatter 76 in the curve makes it uncertain which period is the best fit. The mean magnitude of the variable places it along the HB of NGC 6388. 5.4 Reddening Reddenings for the RRab stars of NGC 6388 were determined using Blanco’s method as outlined in Section 4.5. Making use of the averaged photometry of the (B — V) light curve in the phase range, 0.5-0.8 after maximum light, the reddenings for the RRab stars with good light curves were calculated (Table 5.4). The mean reddening value for the 5 RRab stars which are believed to be prob- able members of NGC 6388 is E(B — V) = 0.38 :t 0.02. The range in reddening values accords with previous determinations that NGC 6388 is subject to differential reddening, although the range is not as large as that of NGC 6441. Silbermann et al. determined, in a similar fashion, that the reddenings for V17 and V29 are 0.48 and 0.47, respectively, with uncertainites of :l:0.04. A source of the discrepancies between the reddenings determined by this survey and that of Silbermann et al. is their use of AS = 8, corresponding to a metallicity lower than the one adopted in this paper (AS = 3.22). Another explanation for the differences in reddenings found by this survey and Silbermann et al. may be attributed to the high scatter in the light curves found by Silbermann et al. Alcaino (1981) derived the reddening of NGC 6388 to be E(B-V): 0.41 from the color of the giant branch as compared to that in 47 Tuc. Zinn (1980) and Reed et al. (1988) obtained E(B- V)=0.35 and 0.39, respectively, from their analysis of the integrated cluster light. It should be emphasized that the type of RRL in NGC 6388 are different in 77 Table 5.4. NGC 6388: Reddening Determinations ID E(B - V) V17 0.346 V21 0.370 V22 0333 V28 0405 V30 0401 nature to those which Blanco used in establishing his relationship between metallicity, period, and instrinsic color. As was done for NGC 6441, it is assumed that Blanco’s formula applies to the RRab stars in NGC 6388. This may not be the case if, as is presented in this paper, the RRab stars in NGC 6388 are unusually bright for their metallicity. 5.5 Cepheids Four Cepheid variables were found in NGC 6441. The mean properties of these variables are listed in Table 5.5. One of these was already noted as a star showing variability. V18 was listed by Hazen & Hesser (1986) as a star with a period < 2 days. Of the four Cepheids found, 3 have periods of less than 10 days, making them members of the subset of type II Cepheids known as BL Herculis stars. As was noted in Section 5.3, V37 has a period of around 10 days, classifying it as a W Virginis type Type II Cepheid. The properties of the Cepheids are discussed further in Section 6.3. 78 Table 5.5. NGC 6388: Mean Properties of Cepheid Stars ID Period (V) (B—V) AV AB Comments V18 2.85 15.584 0.984 0.77 1.20 V36 3.15 15.530 0.878 1.05 1.45 V37 10.0 14.680 1.196 V38 1.878 1.15 oddly bright? 5.6 Eclipsing Binaries and LPVs A number of eclipsing binary stars were found in our field of view. Of the previously known suspect variables, it was found that V14 is a detached binary. Table 5.6 lists the photometric data for the binary stars found by this suvey. Accurate periods for the detached binaries were difficult to determine due to the sampling of this survey. The time coverage of our observations was not suitable for the detection of long period variables (LPVs). Only two of the previously suspected variables in NGC 6388 were determined to be LPVs by this survey, V4 and V12. Three additional LPVS were found. The LPVs found by this study and their locations can be found in Table 9. 79 Table 5.6. NGC 6388: Mean Properties of Binary Stars ID Period (V) (B — V) Av A 3 Comments V14 2.16 16.157 0.537 1.30 1.30 detached V39 0.412 18.245 1.120 0.46 0.56 contact V40 0.536 17.973 0.773 0.28 0.30 contact V41 0.311 18.782 1.127 0.39 contact V42 1.71 17.341 0.679 2.20 2.80 detached V43 1.82 15.699 0.981 0.48 0.52 detached V44 2.02 19.584 0.821 1.22 1.50 detached V55 0.366 19.420 0.858 0.67 0.72 contact V58 0.324 19.073 1.117 contact 80 Chapter 6 ASPECTS OF THE RRC AND CEPHEID VARIABLES The following sections discuss some of the unusual properties of the variables found in NGC 6388 and NGC 6441, specifically the c-type RRL and the Cepheids. The following chapter discusses, in depth, the prOperties of the ab—type RRL and their use as a tool to understand the properties of the two clusters. 6.1 RRC variables Kemper (1982) showed that there are few metal-rich RRC stars in the solar neigh- borhood. RRLS of any type are rare in the more metal-rich globular clusters. The unusual nature of NGC 6388 and N GC 6441 give us an opportunity to investigate c- type RRL in an environment more metal rich than usually found in globular clusters or in the field. Although the periods of a few of the RRC in N GO 6388 and NGC 6441 do tend to fall at longer values, we see that the mean periods of the RRC stars, (PC), (Table 7.1) are not unusually large for either cluster as compared to values found in Oosterhoff II globular clusters (Sandage 1982). The light curves of the N GC 6388 and NGC 6441 RRC stars seem to have some distinguishing features. As the period goes to longer values, the bump seen during rising brightness tends to be found at earlier phases. For most, but not all, of the 81 shorter period RRC we find the bump occuring at a phase ~0.2 before maximum while for the longer period ones, such as V20 and V32 in NGC 6388, and V69 and V76 in NGC 6441, it occurs at ~O.3 before maximum. V33 (P = 0.558), in NGC 6388, does not show the bump during rising brightness in our photometry. Layden et al. mentioned that the light curves of NGC 6441 RRC stars exhibit longer than usual rise times. They comment that the c-type RRL of NGC 6441 have a phase interval of “rising light” between minimum and maximum brightness greater than ~0.5. While the longer period RRC variables do have rise intervals around 0.5, we find that on average, most were ~0.42-0.45. This is in the higher end of the range listed by Layden and collaborators for RRC variables from the General Catalog of Variable Stars (Kholopov 1985). There seems to be a slight trend of increasing rise time with increasing period. Uncertainty of classification among Layden et al.’s suspected variables may have influenced their conclusions. As noted in the individual comments on the RRL for NGC 6441, only two, or three of the variables Layden and collaborators had as suspected variables were actually of c-type. Layden et al. also noted that the minima for the RRC stars may be uncharac- teristically sharp, pointing to SV3 (V70). We find that SV3 is better classified as an eclipsing binary star. We do not see any unusual sharpness to the minima of the RRC variables. The long periods of V69, in NGC 6441, and V32 and V33, in NGC 6388, result in an unusually short gap between the periods of the longest period RRC star and the period of the shortest period RRab star in both clusters. If the RRab and RRC stars had the same mass and luminosity, and were there a single transition line 82 in effective temperature which divided RRab from RRC pulsators, then we would expect a gap of about 0.12 between the logarithms of the longest period RRC star and the shortest period RRab star (van Albada & Baker 1973). Clearly, we do not see that, indicating that one of those assumptions may be in error. Again, however, the existence of differential reddening in the field makes it difficult to interpret the photometry at the level which one would like in addressing this point. An interesting feature seen in NGC 6388, but not in NGC 6441, is the occurence of “short” period c-type RRL. As seen in the period-amplitude diagram for NGC 6388 (Figure 5.4), the c-type RRL, with the exception of V35, seem to fall into three distinct groups: The “longer” period RRC centered at logP = —0.288, the “intermediate” period RRC centered at logP = —0.459, and the “shorter” period RRC centered at logP = —0.617. There does not appear to be any distinction between the shorter period RRC found in NGC 6388 and the more intermediate period RRC, according to their Fourier parameters, as there is seen when comparing the longer period RRC to the “intermediate” period RRC (see Section 6.2). The light curves of the shorter period RRC seem to show more scatter during maximum light as compared to the light curves of the other RRC members of NGC 6388, and are slightly more asymmetric, although the photometry obtained in this survey is not accurate enough to make a conclusive arguement for this. It is of interest to note that two of the three shorter period RRC stars are fainter than the other probable RRC of NGC 6388, as shown in Figure 5.1. It cannot be determined if this effect is due to the differential reddening in NGC 6388. The two RRC stars, which happen to be the two shortest period RRC, do not fall in the same region of the field for NGC 83 6388. It has been argued by some authors that these short period RRc stars may in fact be pulsating in the second overtone mode (e.g. Clement et a1. 1979, Walker 1994, Walker & Nemec 1996). The MACHO collaboration found a maxima in the RRL period distribution at 0.28 days (Alcock et a1. 1996), arguing that this corresponded to the second overtone, RRe, stars. Alcock et al. found that the RRL located about this range showed skewed light curves, as was modelled by Stellingwerf et al. (1987). However, a case has also been made against these variables being second overtone (RRe) pulsators. Kovacs (1998) argued that these variables are RRC variables at the short period end of the instability strip. It is beyond the scope of this paper to argue for or against the classification of the shorter period RRC type stars as second overtone pulsators. In any case, further observations of these variables would help to improve pulsation models and help explain why such a large range in periods exists (0.2357 - 0.5575 days) in NGC 6388. 6.2 Comparisons to Long Period RR Lyrae in w Centauri w Centauri is a unique globular cluster, containing RRL stars spanning a large range in [Fe/ H] (Freeman & Rodgers 1975; Butler et al. 1978; Rey et al. 2000). Although different from N GC 6441 in many ways, of which its low mean [Fe/ H] is one of the more significant, 0) Cen in some respects is an interesting comparison object for that cluster. Overall, the RRL stars in w Cen are those of an Oosterhoff Type II system. However, as noted by Pritzl et al. (2000), it does contain some long period RRab 84 stars, similar in period and amplitude to those in NGC 6441. Here we note that w Cen also contains a number of RRC variables of unusually long period, similar to V69 and V76 in NGC 6441. Making use of the data from Peterson (1994), we plot the Fourier parameters $21 vs. R21 for w Cen (Figure 6.1). A noticable trend is exhibited here. The longer period RRc variables lie as a distinct group at shorter $21 (< 0521 = 0.25). A similar trend is noticable in Figure 4.3 for NGC 6441 and Figure 5.3 for NGC 6388. In Figure 6.2, we plot some of the RRc stars found in w Cen in a period-amplitude diagram. The periods and amplitudes were taken from Kaluzny et al. (1997). When there was more than one entry for a single star, the values were averaged. The [Fe/H] values come from Rey et al. (2000) and the RRC classifications were taken from Butler et al. (1978). We see that although there seems to be a trend of increasing amplitude, decreasing period with decreasing metallcity, there are some longer period RRC found in the more intermediate metallicity range. It should be noted that we have no direct metallicity measurements for the RRL in NGC 6441 and NGC 6388. In this paper we have assumed them to have the overall cluster [Fe/ H] value. 6.3 Cepheids The occurrence of Type II Cepheids in globular clusters is not uncommon. Yet, if the probable Cepheids found in the field of NGC 6388 are indeed members of this cluster, NGC 6388 would be the most metal-rich globular cluster to contain Cepheids. A review by Harris (1985) listed the globular clusters containing Cepheid (16 GCs) or RV Tauri variables (5 GCS). Harris confirmed that the globular clusters 85 0.6 - 0.4 P .— o N o O: O _ o o 0.2 '- 0 52,2900 0 O ’ o 080% £930.. of? O 00o O l L I O 2 Figure 6.1. A plot of the Fourier parameters for RRL in w Centauri. 86 06 I I I T l I I I I l I I I l I I I I '0 o D l . of 0 ”5‘ Cl D ‘ CID 0.4 — D [:1 El — A El Av - 1:1 O 0.2 - - O 1 1 1 l 1 1 1 1 l 1 1 1 1 l 1 L 1 1 0.3 0.4 0.5 0.6 Period (doys) Figure 6.2. Period-amplitude diagram for the first overtone RRL in w Cen- tauri for stars with [Fe/H]<-1.8 (filled triangles), [Fe/H]>-1.4 (filled circles), and -1.8<[Fe/H]<-1.4 (open squares). 87 which contained Type II Cepheids also have blue horizontal branches (Wallerstein 1970). It was further noted by Harris that BL Her, Type II Cepheids with periods < 10 days, may be most frequent in clusters which have extended blue tails on the horizontal branch. Smith & Wehlau (1985) found, by plotting the B / (B + R) fraction for a globular cluster (where B is the number of stars blueward of the RRL gap and R is the number of stars redward of the RRL gap) against the metallicity found for that cluster, that all of the globular clusters known to contain Cepheids have B/ (B + R) > 0.50. The reverse is not true. All clusters with B / (B + R) do not contain Cepheids. Smith & Wehlau also noted that W Vir stars, Type II Cepheids with periods > 10 days, tend to be in the most metal-rich of the globular clusters which have blue HBs. Finally, it was also shown that the clusters which do have Cepheids are also the brighter, more massive, clusters, especially those clusters which have two or more Cepheids. NGC 6388 does exhibit some of the features listed above. It does have a blue component to its HB as seen in its CMD. The B / (B+R) fraction was not determined for NGC 6388 in this study, due to the high contamination from field stars. The high number of BL Her stars found in NGC 6388 agrees with Harris’ idea that they are more frequent in clusters with extended blue tails. NGC 6388 is also one of the brightest globular clusters known in the Galaxy, confirming the tendancy of clusters containing Cepheids to be brighter than those that do not. An interesting question to ask is: Why does NGC 6388 contain Cepheid stars, but NGC 6441 does not? It is possible that our survey was incomplete in finding any Cepheids in NGC 6441, but this doesn’t seem to be the case since no Cepheids 88 were found in the survey of Layden et al. (1999), either. Assuming that our survey was complete, and no Cepheids occur in N GC 6441, the answer to this question may give hints as to the origin of the Cepheids. Both clusters are among the brightest known and both have similar blue extensions to their HBs. Along with having similar metallicities, it would seem that if one of this pair of clusters contained Cepheids, the other would have them too. Harris has explained that some clusters with blue extensions to their HBs, or which have a high B / (B + R), contain Cepheids while others do not may be a consequence of the existence of a very blue tail to the HB. In other words, the presence of a blue tail may promote the production of Cepheids. It was suggested by Smith & Wehlau, from the models of Mengel (1973) and Gingold (1976), that Type II Cepheids may evolve from horizontal branch stars which already have low envelope masses. Sweigart & Gross (1976) predicted that clusters with blue horizontal branches and higher metal abundances would produce horizontal branch stars with especially low envelope masses. This may explain the difference between NGC 6388 and NGC 6441. It can be seen in the CMDS for NGC 6388 and NGC 6441, by Rich et al. (1997), that the blue “tail” in NGC 6388 appears to be more populated than in NGC 6441. A similar effect may be seen in comparing Figures 3.1c and 3.2c. 89 Chapter 7 CLASSIFICATION OF NGC 6388 AND NGC 6441 7 .1 Introduction Oosterhoff (1939) called attention to a dichotomy in the properties of RR Lyrae stars (RRLS) belonging to five RR Lyrae-rich globular clusters. The five clusters could be divided into what are now known as Oosterhoff groups I (00 I) and II (00 II) on the basis of the mean periods and relative proportions of their RRab and RRC stars (Table 7 .1). Subsequent investigations confirmed that all Galactic globular clusters which contain significant numbers of RRLS could be assigned to either 00 I or 00 II. It also became clear that globular clusters of 00 I were more metal rich than those of 00 II (Smith 1995 and references therein). The cause of the Oosterhoff dichotomy, and its implications for the brightnesses of RRLS and the ages of globular clusters, remains a subject of debate (van Albada & Baker 1973; Sandage, Katem, & Sandage 1981; Castellani 1983; Renzini 1983; Lee, Demarque, & Zinn 1990; Sandage 1993a,b; Clement & Shelton 1999). Although RRLS more metal rich than [Fe/ H] = —0.8 are known to exist in the field population of the Galaxy (Preston 1959; Layden 1994), very few RRLS have been discovered within the most metal rich globular clusters. As we have noted metal-rich 90 Table 7.1. Cluster Properties Cluster Type [Fe/H] (Fab) (PC) Nc/NRR M3 00 I —1.6 0.56 0.32 0.16 M15 00 II —2.2 0.64 0.38 0.48 NGC 6441 ? ——0.5 0.75 0.38 0.31 NGC 6388 ? —0.6 0.76 0.36 0.67 clusters usually have stubby horizontal branches which lie entirely or almost entirely to the red side of the instability strip. As shown above, the globular clusters NGC 6388 and NGC 6441 are prominent exceptions to this rule. We reiterate below the conclusion of Pritzl et al. (2000) that NGC 6388 and NGC 6441 do not fit into either the 00 I or 00 II groups. 7 .2 Oosterhoff Classification of NGC 6388 and NGC 6441 Mean properties of RRLS in NGC 6388 and NGC 6441 are summarized in Table 7.1, together with those of the RRLS in M3 and M15, typical 00 I and 00 II clusters. NGC 6388 and NGC 6441 are distinguished by the surprisingly long mean periods of their RRab stars. From what is known of metal-rich field RRLS, one would expect the mean period of their RRab stars to be even shorter than those of Oosterhoff type I globular clusters. Instead, the long mean periods of their RRL, and their high Nc/Ntot value (where NC is the number of RRc stars and NW is the total number of RRL in the system), are closer to the values expected in a metal-poor Oosterhoff II globular cluster. Their value of (Pub) is long even for Oosterhoff II systems. 91 I j T I —' j j I I I I r I I I O N6441 N6388 >|< >k fl< Ooll >|< >|< at L L L I L I I I I I I I I I 0.6 0.7 (Pub) 4% It, IIIIITIIII'IIII'IrIr'I .0 on Figure 7.1. Mean period vs. [Fe/ H] diagram showing the offset of NGC 6388 (circle) and NGC 6441 (square) from the Oosterhoff I (crosses) and Oosterhoff II (asterisks) globular clusters. Data for the Oosterhoff clusters are taken from Sandage (1993a). 92 The distinction of NGC 6388 and NGC 6441 in the Oosterhoff classification scheme is further emphasized in Figure 7.1, where we plot the mean periods of the RRab stars in NGC 6441 and 00 I and 0011 globular clusters, as a function of their parent cluster metallicity. NGC 6388 and NGC 6441 stand out sharply from the other clusters as not only the most metal-rich clusters plotted, but also as the clusters with the largest values of (Pa ). As shown, this completely contradicts the trend seen among the other clusters, with the more metal-rich globular clusters having shorter periods on average. It should be noted that the mean period for the RRab stars in NGC 6388 shown in Figure 7.1 was determined without including V30 (due to its uncertain period), giving a value of 0.713 days. When V30 is included, the mean period is 0.758 days. With our current understanding of the RRC variables found in these clusters, we have updated the period histograms of Pritzl et al. (2000) for NGC 6388 and NGC 6441 in Figure 7.2. Like the very metal-poor 00 II clusters, NGC 6388 and NGC 6441 are relatively rich in RRc stars. On the other hand, as has already been noted, the metallicities of NGC 6388 and NGC 6441 are similar to, but even higher than, those of 00 I clusters. Again, NGC 6388 and NGC 6441 stand out as anomalous. The period-amplitude diagram provides a way to look at the general trends of the RRL in a system without having to worry about reddening. In Figure 7.3 we revisit the diagram presented in Pritzl et al. (2000), comparing NGC 6388 and NGC 6441 to other globular clusters and field stars of similar metallicity. The usual differences between the Oosterhoff groups are apparent in this figure. At constant amplitude, RRab stars in the 00 II clusters M15 (Silbermann et al. 1995; Bingham et al 1984) 93 I I I I I I I T M3 M15 :5 __ NRR=I75 _ __ NRR=74 _, 01 ,_ __ _. O F— L— Q) .C) 3 Z CD 0 I #1 I F > .4: 9 NGC 5388 NGC 6441 <1) 0: :3 _ NRR=14 _._ NRR=36 - “l a .... .4 O O L 0.2 0.4 0.67 0.8 1 0.2 0.4 0.6 i 0.8 1 Period (doys) Figure 7.2. Period histograms for M15, M3, NGC 6388, and NGC 6441. The filled area represents the c-type RR Lyrae. The open area represents the ab—type RR Lyrae. Data for M3 and M15 are taken from Clement (1999b). 94 l ' l ' l 1.5 - : ** >I< . *3?" U P >12" 91— >1< 2- + * < I- 0.5 - O - l m l 1 I. -O.4 -O.2 0 log P Figure 7 .3. Period-amplitude diagram for the ab-type RR Lyrae variables of NGC 6388 (open circles) and NGC 6441 (filled circles) as compared to field RR Lyrae of [Fe/H] 2 -0.8 (asterisks), V9 in 47 The (six pointed star), M3 (open boxes), M15 (stars), and M68 (triangles). The small filled circles denote variables in NGC 6441 that are believed to be blended with companions or possibly to be Blazhko stars. 95 and M68 (Walker 1994) are shifted toward longer periods compared to those in the 00 I cluster M3 (Carretta et al. 1998), while metal-rich field RRab stars occur at shorter periods. As compared to the field stars of similar metallicity, the RRL of NGC 6388 and NGC 6441, at a given amplitude, fall at unusually longer periods. They even fall at periods as long as, and in some cases longer than, those of 00 II RRab stars. It should be noted that, in selecting comparison stars to plot in Figure 7.3, obvious Blazhko variables have been excluded, but no other stringent light curve criteria have been applied. We note that we have assumed in this discussion that the metal-abundance of the RRL stars in NGC 6388 and NGC 6441 are the same as that found by Armandroff & Zinn (1988) for the cluster as a whole. It is worth mentioning, however, that as yet we have no direct measurement of metallicity for individual RRL stars. The period shift of the RRab stars in NGC 6441 relative to the RRab stars of equal B amplitude in the globular cluster M3 (from Sandage et al. 1981) is about 0.08 in log P. If the masses of the RRab stars in M3 and NGC 6441 were the same, this would correspond to a difference of Alog L=0.10 or AMboz=0.24. This, admittedly simplified, analysis would make the RRab stars in NGC 6441 slightly more luminous than the RRab stars within the Oosterhoff II cluster M15. RRab star periods longer than 0.8 days account for 60 and 32 percent of the RRab stars in NGC 6388 and NGC 6441 respectively. Such long periods are rare but not unprecedented among other globular clusters. The globular cluster 02 Centauri, unique in containing RRLS with a wide range in measured [Fe/ H] (Butler, Dickens, & Epps 1978), also contains a significant number of very long period RRab stars. 96 Although 02 Cen is primarily an 00 II cluster, it has been suggested that it contains RRLS belonging to both Oosterhoff groups (Butler et al. 1978). However, most of its RRab stars have periods much shorter than those in NGC 6388 and NGC 6441. As another example, Wehlau (1990) found that the three RRab stars in the globular cluster NGC 5897 all have periods longer than 0.79 d. NGC 5897 is a metal-poor cluster, however, with [Fe/H] = —1.68 (Zinn & West 1984), and in that regard is unlike NGC 6388 and NGC 6441. With a period of 0.737d, the RRL V9 in the metal-rich globular cluster 47 Tue may be a closer analogue to the RRab stars in NGC 6388 and NGC 6441 (Figure 3 of Sweigart & Catelan 1998b; Carney et al. 1993) We conclude that NGC 6388 and N GC 6441 cannot be readily classified as either 00 I or 00 II from the properties of their RRLS. The long mean periods of their RRab stars, their location in the period-amplitude diagram, and the large proportions of RRC stars all support an 00 II classification (see also Clement 1999a). However, the mean RRab periods are longer than for 00 II clusters and the high metallicities of NGC 6388 and NGC 6441 stand in contradiction to the low metallicities of 00 11 systems. We also note that NGC 6388 and NGC 6441 are very different from the globular clusters of the Large Magellanic Cloud, which do not fall into either 00 group (Bono, Caputo, & Stellingwerf 1994). Those clusters are metal-poor and have values of (Feb) intermediate between 00 I and 00 II. We therefore suggest that NGC 6388 and NGC 6441 might represent a new Oosterhoff class. 97 7 .3 The Luminosity of the RR Lyrae Stars As mentioned above, Sandage et al. ( 1981) noted a shift in period between RRLS in M3 and M15, measured at constant Tag or constant amplitude. Using Ritter’s relation, P\/(p) = Q, they interpreted this as evidence that the M15 RRLS were less dense and thus more luminous than those in M3. This was later generalized to a luminosity-metallicity correlation, in the sense that RRL brightness increases with decreasing [Fe/H] (Sandage 1982; Carney et al. 1992). This luminosity-metallicity correlation is generally represented by a linear equation of the form My 2 a x [Fe/ H] + B, where a denotes the sensitivity of RRL luminosity to metallicity. The size of this correlation remains subject to debate, with values of oz ranging from 0.3 (Sandage 1993b) to 0.13 (Fusi Pecci et al. 1996). On the basis of this prior work, one would expect the locus of RRab stars in the period-amplitude diagram to shift to shorter periods with increasing [Fe/H]. Com- parison of the locations in the period-amplitude diagram of RRab stars in the very metal-poor globular clusters M15 and M68 with RRab stars in M3 and with metal- rich field RRab stars (Figure 7.3) confirms this expectation. On the other hand, RRab stars in NGC 6388 and NGC 6441 are shifted toward longer periods than would be expected from their metallicities, indicating that they are at least as bright as RRLS in very metal-poor 00 II clusters. Sweigart & Catelan (1998b), in an effort to explain the unusual slope of the H83 of these two clusters, created three theoretical scenarios which could be tested using RRLS (see Chapter 1). Their models predict that the blue HBs of NGC 6388 and 98 NGC 6441 should be unusually bright. Though at the time, the data available on the RRLS of the two clusters were slight, available observations were consistent with the predictions of these models. The data now available make the case much more strongly. The boxed area in Figure 7.3 represents one of the model predictions (helium-mixing scenario) of Sweigart & Catelan [1998b, from their Figure 3 as translated to the period-amplitude diagram by Layden et al. (1999, cf. their Figure 9)]. The period-amplitude data are in similarly good agreement with the other scenarios of Sweigart & Catelan, all of which require that the RRLS of NGC 6388 and NGC 6441 are brighter than solar neighborhood field RRLS of comparable [Fe/ H] It has been argued that HB evolution, rather than metallicity per se, might be the governing factor in determining whether a cluster belongs to 00 I or 00 II (Clement & Shelton 1999; Lee & Carney 1999). Lee et al. (1990) also argued that evolution was an important element in the origin of the Oosterhoff phenomenon. 00 II clusters usually have bluer HBs than 00 I clusters, although there are exceptions such as M28 or NGC 4147 (cf. Table 1 in Castellani & Quarta 1987). According to this explanation RRLS in 00 II clusters spend most of their HB lifetimes on the blue HB (BHB) before evolving redward through the instability strip on their way back to the asymptotic-giant branch. The final crossing of the instability strip occurs at a brighter luminosity and hence longer period than for stars near the ZAHB. NGC 6388 and NGC 6441 have predominantly red HBs with pronounced blue components. The sloping HB morphology in the color-magnitude diagrams of NGC 6388 and NGC 6441 does not indicate that the RRLS in those clusters have evolved 99 from the BHB. Moreover, Sweigart & Catelan’s (1998b) models indicate that the RRLS are in the main phase of HB evolution, requiring that the HBs of the clusters are unusually bright. Thus, evolution does not appear to be the explanation for the long RRL periods in NGC 6388 and NGC 6441. The HB morphology of the two clusters, together with the theoretical scenarios of Sweigart & Catelan, further lead us to conclude that the bright RRLS are a consequence of bright HBs rather than evolution from the BHB. 7.4 Discussion The relatively metal-rich globular clusters NGC 6388 and NGC 6441 are distinct in several ways from ordinary 00 I and 00 II clusters. Nor are their RRLS similar to those of the metal-rich field population of the solar neighborhood. The location of NGC 6388 and N GC 6441 RRab stars in the period-amplitude diagram is consistent with the RRLS of the two clusters being as bright or slightly brighter than those of 00 11 clusters such as M15 or M68, a result consistent with the theoretical mod- els of Sweigart & Catelan (1998b). The RRLS in NGC 6388 and NGC 6441 thus demonstrate that RRL luminosity is not always inversely correlated with metallicity. Should we then regard NGC 6388 and NGC 6441 as sufficiently distinct from 00 I and 00 II clusters to be representatives of a third Oosterhoff group? Or should we instead regard them as an aberrant type of 00 II cluster? It is to some degree a matter of semantics, the answer depending in part upon which characteristics one regards as essential to Oosterhoff classification and upon the physics of the system. It is nonetheless worth noting that NGC 6388 and NGC 6441 are alike in ways other 100 than [Fe/ H] and the properties of their RRLS. Both are among the most luminous globular clusters of the Galaxy and both have very high central densities. It remains an open but intriguing question whether those attributes play a role in producing the unusual RRL populations of the clusters. Possibly the most interesting result to come from the comparison of N GC 6388 and N GO 6441 to other Galactic globular clusters concerns the metallicity-luminosity relation. RR Lyrae stars are used as standard candles to Population II systems. It has been thought, as seen in Figure 7.3, that the more metal-poor an RR Lyrae, the longer its period is, and therefore, the more luminous it is. As mentioned above, the luminosity-metallicity correlation is generally represented by a linear equation of the form My 2 a x [Fe/ H] + B. If the more metal-rich RRL are indeed the less luminous, they should have shorter periods than RRL in more metal-poor clusters - all else being equal. Clearly, the RRL of NGC 6388 and NGC 6441 do not follow such a relation, falling at periods as great, if not greater, than the RRL in the more metal-poor globular clusters. There is thus no universal correlation between RRL luminosity and metallicity, assuming the metallicity of the RRLS in NGC 6388 and NGC 6441 are the same as those of the clusters as a whole. 101 Chapter 8 SUMMARY AND CONCLUSIONS NGC 6388 and NGC 6441 stand out as two of the more unique globular clusters of our Galaxy. NGC 6388 and N GC 6441 are confirmed to be metal-rich globular clus- ters exhibiting unusual horizontal branch morphology. A strong red component of the horizontal branch is seen, as is expected for clusters in this metallicity range. In addi- tion to the red clump, both clusters have blue horizontal branches extending through the instability strip which are not found in other clusters of similar metallicities, i.e., NGC 6388 and NGC 6441 exhibit a second-parameter effect. The explanations of such an effect may be constrained by the sloped nature of the horizontal branches, getting brighter in V with decreasing B — V, as Sweigart & Catelan suggested. The number of variable stars known in each cluster has been doubled. The number of RR Lyrae stars found in NGC 6388 and NGC 6441 has been increased to 15 and 40, respectively. As predicted by Sweigart & Catelan (1998b), the periods of the RR Lyrae are unusually long for clusters of their metallicity, a result confirmed and extended in the period amplitude diagram comparing NGC 6388 and NGC 6441 to other globular clusters. A few long period RRC stars were also found to exist in each cluster, resulting in a smaller than expected gap between the longest period RRC and the shortest period RRab stars. 102 NGC 6441 was found to contain a number of fundamental mode RR Lyrae that are both brighter and redder than the other probable RRab found along the horizontal branch. This effect is likely due to blending with unresolved red companion stars. The reddening determined for NGC 6441 is E (B — V) = 0.53 :l: 0.02 with significant differential reddening across the cluster. From the RR Lyrae in the cluster, excluding the brighter and redder RRab stars, the mean magnitude of the horizontal branch was determined to be 17.417 i 0.298 mag. NGC 6388 was found to contain, in addition to its long period RR Lyrae, a small number of short period (0.2357 - 0.2512 days) RRc stars. Of more interest is the occurrence of Type II Cepheids in NGC 6388, making it the most metal- rich globular cluster to contain Cepheid variables. The idea that globular clusters containing Cepheids tend to have blue tails to their horizontal branches is supported. A mean reddening of E (B — V) = 0.38 i 0.02 was found for NGC 6388. The mean magnitude of the horizontal branch in NGC 6388 was determined to be 16.892i0.239, using the RR Lyrae stars. NGC 6388 and NGC 6441 are also shown to stand apart from other Galactic globular clusters in that they do not fit in the Oosterhoff classification scheme. The mean periods of the RR Lyrae in each cluster are even longer than the typical, more metal-poor, Oosterhoff Type II clusters. This contradiction in the trend of increasing period with the decrease in metallicity, for a given amplitude, implies the metallicity- luminosity relationship for RR Lyrae stars is not universal. 103 APPENDIX A ADDITIONAL TABLES 104 Table A1. NGC 6388: Comparison of Photometry with Alcaino. Pritzl et al. Alcaino ID (V) (B) (V) (B) L 13.739 14.776 13.76 14.80 M 13.815 14.427 13.85 14.47 R 14.922 17.023 15.02 17.06 T 15.299 16.883 15.40 16.91 U 15.604 17.322 15.66 17.49 V 15.831 17.718 15.90 17.61 W 15.868 17.195 15.92 17.34 X 15.995 16.986 16.03 16.97 Y 16.171 17.452 16.20 17.44 Z 16.276 16.751 16.37 16.77 105 Table A2. NGC 6388: Comparison of Photometry with Silbermann et al. Pritzl et al. Silbermann et al. “3 (V) (B) (V) (B) 16.89 1.45 16.91 1.44 17.08 1.39 17.04 1.35 17.20 1.20 17.25 1.32 17.55 0.34 17.53 0.31 17.01 1.44 17.09 1.33 9 16.99 1.10 16.98 1.07 10 14.36 0.74 14.36 0.71 12 18.20 1.17 18.17 1.30 13 16.57 1.49 16.64 1.51 14 17.17 1.17 17.21 1.07 15 17.19 1.20 17.29 1.09 19 16.42 1.60 16.42 1.62 20 17.20 1.14 17.30 1.07 23 16.54 1.56 16.58 1.60 26 16.67 0.77 16.59 0.85 28 17.89 1.32 17.86 1.23 29 16.21 1.25 16.19 1.34 30 16.61 0.91 16.61 0.86 34 16.80 1.31 16.73 1.31 35 16.09 1.54 16.14 1.55 38 14.14 1.79 14.20 1.82 40 17.29 1.22 17.28 1.35 41 16.20 1.60 16.21 1.61 42 15.66 1.80 15.61 1.70 43 16.96 1.50 17.02 1.46 45 17.40 1.24 17.50 1.16 46 17.38 1.17 17.34 1.13 48 17.35 1.42 17.38 1.40 49 15.59 1.29 15.58 1.27 51 14.20 0.72 14.24 0.60 52 16.34 1.18 16.38 1.11 53 16.58 1.15 16.60 1.13 56 17.31 1.16 17.36 1.28 58 16.10 1.58 16.10 1.55 60 17.02 0.94 16.91 1.00 61 15.96 1.38 15.97 1.34 OOGI-ROOI—t 106 Table A2 (cont’d). N GC 6388: Comparison of Photometry with Silbermann et al. Pritzl et al. Silbermann et al. ID (V) (B) (V) (B) 62 17.13 1.32 17.20 1.26 64 15.45 1.83 15.45 1.87 66 17.07 1.08 17.11 1.02 67 15.66 1.71 15.71 1.77 68 16.01 1.20 16.03 1.14 69 16.17 1.56 16.25 1.57 70 16.64 1.12 16.67 1.12 71 17.61 1.22 17.70 1.31 72 15.90 0.89 15.89 0.87 73 17.30 1.14 17.30 1.09 74 17.24 1.15 17.33 1.15 75 16.18 1.59 16.24 1.63 76 17.36 1.17 17.43 1.11 80 17.06 1.14 17.14 1.15 82 17.17 1.27 17.25 1.14 83 17.30 1.17 17.34 1.09 84 17.65 1.37 17.77 1.27 85 17.36 1.35 17.41 1.37 86 17.21 1.17 17.31 1.07 87 17.66 0.99 17.69 1.08 89 17.36 1.33 17.41 1.32 90 17.21 0.94 17.27 0.89 91 14.89 1.98 15.00 2.18 92 17.15 1.16 17.17 1.12 94 17.30 1.32 17.30 1.38 95 18.27 0.86 18.28 1.01 96 17.16 1.18 17.22 1.20 98 17.63 1.00 17.64 0.99 99 14.77 1.42 14.78 1.41 100 17.02 1.19 17.07 1.08 101 17.20 1.16 17.30 1.20 105 17.16 1.11 17.20 1.07 106 17.25 1.43 17.30 1.42 107 18.23 1.13 18.11 1.11 108 16.79 1.38 16.76 1.29 109 16.36 1.40 16.39 1.51 107 Table A2 (cont’d). N GC 6388: Comparison of Photometry with Silbermann et al. Pritzl et al. Silbermann et al. ID (V) (B) (V) (B) 110 15.99 1.60 16.05 1.52 111 17.12 1.18 17.05 1.13 113 17.69 1.39 17.70 1.39 116 16.54 1.22 16.59 1.13 120 16.24 1.54 16.25 1.54 122 16.82 1.36 16.86 1.36 124 16.91 1.18 16.92 1.16 125 17.69 1.30 17.74 1.34 127 17.19 1.24 17.26 1.22 128 15.58 1.16 15.61 1.13 130 16.07 1.52 16.13 1.47 131 16.98 1.29 17.08 1.24 132 17.34 1.22 17.33 1.14 133 16.02 1.59 16.03 1.61 134 15.71 1.38 15.64 1.46 136 16.97 1.08 17.02 1.05 137 16.57 1.58 16.46 1.57 138 15.08 1.88 15.09 1.98 139 17.62 1.19 17.63 1.09 140 17.74 1.24 17.82 1.19 141 15.42 0.80 15.35 0.70 143 17.29 1.41 17.27 1.31 144 17.13 1.12 17.19 1.04 147 17.42 1.19 17.51 1.13 148 15.52 1.56 15.57 1.57 151 17.10 1.30 17.14 1.25 152 17.12 1.30 17.12 1.24 153 15.18 1.84 15.12 1.75 154 15.00 1.91 14.97 1.82 162 16.39 1.54 16.40 1.50 164 17.82 1.25 17.85 1.30 165 16.71 1.06 16.74 0.97 170 17.17 1.17 17.28 1.11 174 16.87 0.88 16.93 0.80 180 15.31 1.93 15.33 1.96 181 16.49 1.27 16.54 1.22 108 Table A2 (cont’d). N GC 6388: Comparison of Photometry with Silbermann et al. Pritzl et al. Silbermann et al. ID (V) (B) (V) (B) 182 16.59 1.34 16.57 1.37 188 16.34 1.52 16.37 1.54 190 15.80 1.77 15.79 1.82 191 16.15 1.51 16.27 1.42 194 17.15 1.19 17.12 1.14 195 17.03 1.14 17.06 1.05 196 16.27 1.46 16.31 1.42 197 17.32 1.16 17.38 1.16 198 15.61 1.58 15.62 1.57 200 17.33 1.19 17.38 1.25 204 15.58 1.74 15.64 1.63 205 17.62 1.34 17.56 1.33 207 16.66 1.59 16.70 1.65 210 17.33 1.25 17.37 1.20 212 16.14 1.52 16.12 1.59 213 17.19 1.37 17.23 1.30 216 15.70 1.72 15.80 1.77 217 17.30 1.29 17.34 1.41 219 16.19 1.52 16.12 1.51 221 17.66 1.38 17.76 1.36 222 17.52 1.16 17.54 1.24 224 17.38 1.29 17.43 1.22 225 15.45 0.99 15.45 0.95 237 15.58 1.62 15.61 1.65 240 17.30 1.03 17.32 1.08 244 17.47 1.29 17.43 1.23 245 16.05 1.53 16.07 1.46 246 17.06 1.16 17.09 1.07 247 15.50 1.89 15.52 1.99 250 16.67 1.54 16.69 1.60 251 16.58 1.56 16.64 1.50 252 16.78 1.50 16.81 1.42 253 16.56 1.41 16.50 1.51 257 15.35 1.81 15.44 1.87 264 15.95 1.54 15.92 1.68 268 15.02 1.97 15.04 1.93 109 Table A2 (cont’d). NGC 6388: Comparison of Photometry with Silbermann et al. Pritzl et al. Silbermann et al. ID (V) (B) (V) (B) 276 16.49 1.53 16.45 1.73 277 12.99 0.58 12.99 0.55 279 15.56 1.57 15.51 1.61 285 16.42 1.56 16.36 1.50 291 17.32 1.25 17.39 1.18 292 16.48 0.90 16.52 0.80 294 16.54 1.57 16.58 1.56 297 17.36 1.20 17.34 1.32 298 15.88 1.51 15.82 1.47 299 16.26 1.53 16.27 1.49 301 15.35 1.75 15.38 1.77 302 17.20 1.09 17.28 1.19 303 15.40 1.96 15.36 2.04 306 16.11 1.42 16.07 1.35 308 16.98 1.14 17.00 1.08 311 17.09 1.15 - 17.06 1.13 314 16.97 1.71 17.02 1.78 315 17.36 1.25 17.41 1.16 320 18.08 1.18 18.04 1.12 321 17.29 0.39 17.33 0.34 322 15.65 1.46 15.67 1.43 323 18.15 0.92 18.25 0.85 324 16.83 1.10 16.84 0.98 326 17.29 1.24 17.34 1.29 327 17.26 1.18 17.20 1.12 329 16.27 1.60 16.25 1.61 331 16.93 1.11 16.97 1.00 332 16.34 1.34 16.34 1.32 334 17.62 1.31 17.69 1.22 336 17.17 1.13 17.21 1.17 337 15.70 1.80 15.78 1.83 338 15.93 1.59 15.97 1.57 339 17.18 1.27 17.15 1.21 340 16.98 1.13 17.06 1.05 341 17.20 1.18 17.21 1.18 342 17.06 1.13 16.96 1.19 110 Table A2 (cont’d). NGC 6388: Comparison of Photometry with Silbermann et al. Pritzl et al. Silbermann et al. ID (V) (B) (V) (B) 343 17.02 1.16 17.02 1.12 344 15.17 1.24 15.20 1.18 346 17.11 1.11 17.11 1.11 347 17.00 1.21 17.02 1.11 350 16.03 1.33 16.06 1.23 357 17.39 1.16 17.38 1.14 359 15.46 1.78 15.42 1.75 360 16.70 1.33 16.69 1.34 361 14.97 2.11 14.92 2.08 362 16.43 1.15 16.45 1.10 366 16.98 1.19 16.95 1.23 367 17.12 1.19 17.20 1.13 369 17.24 1.21 17.18 1.09 372 17.26 1.22 17.36 1.13 375 17.38 1.39 17.27 1.30 380 15.84 1.03 15.88 0.96 383 17.65 1.32 17.68 1.22 384 16.46 1.26 16.46 1.16 387 17.16 1.21 17.22 1.29 389 17.26 1.14 17.36 1.03 393 16.59 1.46 16.61 1.45 394 18.11 1.25 18.01 1.15 395 17.03 0.45 17.10 0.34 396 16.71 1.33 16.70 1.43 397 14.57 0.74 14.57 0.70 399 16.89 0.37 16.94 0.26 402 16.37 1.43 16.44 1.38 403 17.27 1.25 17.33 1.21 404 16.23 1.40 16.23 1.42 405 15.35 1.45 15.36 1.43 407 16.52 1.46 16.51 1.48 111 Table A3. NGC 6388: Comparison of Photometry with HST. Pritzl et al. HST (V) (B) (V) (B) 16.093 17.775 16.199 17.856 17.650 19.063 17.667 19.042 16.417 17.975 16.464 17.989 17.290 18.524 17.390 18.620 15.024 16.994 15.100 17.025 16.078 17.703 16.174 17.765 17.023 18.190 17.118 18.250 14.852 16.827 14.938 16.819 17.378 18.651 17.430 18.672 Table A.4. NGC 6441: Comparison of Photometry with HST Pritzl et al. HST Layden et al. (V) (B) (V) (B) (V) 17.872 19.284 17.968 19.305 17.500 15.837 17.854 15.921 17.835 15.506 17.998 19.441 18.038 19.451 17.631 17.965 19.376 17.981 19.339 17.525 18.370 19.824 18.476 19.897 17.976 16.333 17.905 16.428 17.943 15.988 17.876 19.307 17.868 19.252 17.457 17.954 19.366 17.994 19.361 17.538 18.193 19.682 18.193 19.610 17.840 17.947 19.299 17.986 19.311 17.511 18.317 19.815 18.416 19.832 17.912 17.178 19.091 17.234 19.031 16.828 17.793 19.229 17.829 19.175 17.793 18.133 19.376 18.041 19.386 17.494 112 Table A5. NGC 6441: Comparison of Photometry with Hesser & Hartwick Pritzl et al. Hesser& Hartwick Layden et al. ID (V) (B) (V) (B) (V) 4 14.740 15.529 14.76 15.55 14.353 6 14.042 14.753 14.04 14.74 13.666 8 15.694 17.386 15.69 17.34 15.320 10 16.132 17.996 16.23 17.96 15.754 12 16.229 18.128 16.28 18.25 15.872 14 17.081 18.512 16.96 18.43 16.730 18 15.908 17.799 15.94 17.84 15.519 20 16.667 17.755 16.74 17.83 16.306 30 15.679 17.406 15.77 17.51 15.335 31 15.567 16.388 15.56 16.41 15.219 33 14.922 15.986 14.95 16.00 14.576 35 15.921 18.020 16.05 18.11 15.679 37 16.094 17.907 16.17 17.96 15.744 38 16.007 17.062 16.12 17.14 15.612 42 16.632 18.235 16.69 18.30 16.246 43 16.041 16.984 16.07 16.99 15.651 51 15.555 17.141 15.58 17.22 15.145 112 15.623 16.702 15.53 16.64 15.265 113 Table A6. NGC 6441: Photometry of the Variable Stars (V) HJ D 2450000 V1 V2 V5 V6 V9 V10 V37 V38 959.663 959.731 960.667 961.831 961.863 962.584 962.630 962.670 962.752 962.789 962.823 962.861 965.590 965.626 965.674 965.712 965.744 965.776 965.809 965.842 966.575 966.607 966.615 966.647 966.684 966.716 966.761 966.797 966.823 966.856 967.578 967.610 967.642 967.684 967.756 967.787 967.823 967.857 968.570 968.603 968.644 968.676 968.725 968.770 968.803 16.736 16.687 16.700 16.794 16.815 16.863 16.839 16.850 16.864 16.837 16.853 17.035 17.012 17.056 17.021 17.011 17.006 17.026 17.011 17.062 17.069 17.073 17.066 17.056 17.060 17.057 17.138 17.062 17.081 17.081 17.120 17.145 17.106 17.103 17.129 17.119 17.114 17.150 17.119 17.149 17.145 17.145 17.154 17.133 17.570 17.410 17.161 17.357 17.228 17.303 17.425 17.534 17.511 17.388 17.339 17.272 17.217 17.344 17.374 17.434 17.472 17.554 17.561 17.565 17.620 17.606 17.479 17.344 17.299 17.187 17.197 17.205 17.283 17.212 17.251 17.344 17.449 17.549 17.530 17.437 17.341 17.554 17.409 17.316 17.213 17.190 17.257 17.245 15.416 15.415 15.346 15.286 15.231 15.238 15.264 15.263 15.264 15.261 15.254 15.111 15.128 15.113 15.118 15.120 15.122 15.126 15.123 15.097 15.094 15.096 15.102 15.113 15.100 15.119 15.073 15.085 15.093 15.085 15.093 15.098 15.088 15.071 15.087 15.072 15.086 15.039 15.031 15.051 15.036 15.041 15.042 15.031 14.174 14.177 14.201 14.243 14.286 14.266 14.188 14.214 14.159 14.268 14.225 14.275 14.603 14.566 14.611 14.644 14.629 14.609 14.598 14.615 14.714 14.726 14.731 14.661 14.611 14.718 14.579 14.805 14.732 14.766 14.776 14.776 14.785 14.807 14.856 14.776 14.843 14.817 14.952 14.939 14.957 14.958 14.970 14.966 14.955 15.223 15.220 15.176 15.145 15.069 15.083 15.086 15.083 15.080 15.075 15.068 14.938 14.934 14.878 14.944 14.932 14.929 14.919 14.919 14.862 14.886 14.882 14.877 14.878 14.873 14.879 14.888 14.868 14.863 14.823 14.827 14.830 14.839 14.822 14.837 14.826 14.825 14.774 14.771 14.794 14.782 14.785 14.779 14.782 16.954 16.952 16.933 16.934 16.916 16.868 16.890 16.893 16.893 16.896 16.888 16.884 16.790 16.801 16.782 16.818 16.817 16.819 16.815 16.807 16.755 16.768 16.769 16.781 16.782 16.787 16.785 16.805 16.782 16.782 16.717 16.739 16.738 16.740 16.743 16.766 16.745 16.742 16.675 16.691 16.708 16.710 16.711 16.713 16.698 17.133 17.391 17.955 17.864 17.931 18.068 17.463 16.907 17.211 17.345 17.448 17.541 18.010 18.072 17.791 17.181 16.909 17.040 17.179 17.308 17.609 17.656 17.665 17.730 17.791 17.847 17.865 17.944 17.993 18.027 16.928 17.028 17.150 17.308 17.503 17.576 17.613 17.677 17.882 17.885 17.964 18.003 17.996 17.365 16.876 17.264 17.367 17.624 17.188 17.255 17.220 17.294 17.345 17.453 17.527 17.548 17.585 17.350 17.400 17.731 17.517 17.546 17.581 17.598 17.641 17.658 17.681 17.699 17.729 17.731 17.798 17.831 17.710 17.412 17.291 17.397 17.143 17.054 17.114 17.248 17.315 17.362 17.421 17.435 17.451 17.508 17.539 17.580 17.619 17.678 114 Table A6 (cont’d). NGC 6441: Photometry of the Variable Stars (V) HJ D 2450000 V39 V40 V41 V42 V43 V44 V45 V46 959.663 959.731 960.667 961.831 961.863 962.584 962.630 962.670 962.752 962.789 962.823 962.861 965.590 965.626 965.674 965.712 965.744 965.776 965.809 965.842 966.575 966.607 966.615 966.647 966.684 966.716 966.761 966.797 966.823 966.856 967.578 967.610 967.642 967.684 967.756 967.787 967.823 967.857 968.570 968.603 968.644 968.676 968.725 968.770 968.803 17.780 17.869 17.991 17.405 17.356 17.360 17.413 17.512 17.568 17.618 17.674 17.921 17.945 17.567 18.032 18.016 17.940 17.684 17.620 18.038 17.966 17.918 17.639 17.567 17.382 17.314 17.360 17.387 17.436 17.339 17.338 17.373 17.432 17.529 17.563 17.620 17.667 17.531 17.557 17.604 17.648 17.692 17.720 17.758 18.023 17.380 17.550 17.409 17.527 17.595 17.703 17.744 17.834 17.897 17.935 16.942 16.970 17.849 17.263 17.359 17.439 17.489 17.527 17.764 17.792 17.793 17.789 17.849 17.926 17.971 18.035 17.910 17.397 17.004 17.117 17.216 17.334 17.469 17.560 17.618 17.705 17.816 17.782 17.871 17.926 17.991 17.845 17.342 16.812 16.846 16.682 16.777 16.807 16.804 16.817 16.802 16.855 16.852 16.883 16.901 16.816 16.820 16.577 16.868 16.871 16.886 16.902 16.906 16.924 16.889 16.875 16.720 16.577 16.496 16.509 16.558 16.586 16.602 16.627 16.643 16.636 16.699 16.765 16.746 16.790 16.788 16.789 16.795 16.829 16.819 16.847 16.874 16.834 17.414 17.474 17.560 17.266 17.605 17.430 17.266 17.178 17.236 17.283 17.340 17.654 17.676 17.428 17.737 17.748 17.770 17.719 17.520 17.786 17.761 17.748 17.588 17.428 17.350 17.185 17.195 17.213 17.239 17.202 17.193 17.217 17.262 17.341 17.395 17.429 17.467 17.382 17.382 17.439 17.462 17.489 17.539 17.532 17.699 17.756 17.538 17.580 17.620 17.555 17.587 17.617 17.663 17.698 17.737 17.794 17.443 17.494 17.728 17.583 17.608 17.634 17.652 17.683 17.647 17.713 17.698 17.698 17.728 17.750 17.795 17.804 17.705 17.478 17.789 17.601 17.467 17.315 17.219 17.276 17.321 17.375 17.328 17.344 17.382 17.437 17.488 17 .530 17.613 16.751 16.352 16.799 16.802 16.848 16.894 16.872 16.285 16.339 16.438 16.551 16.848 16.848 16.886 16.905 16.823 16.539 16.338 16.429 16.681 16.709 16.701 16.720 16.441 16.754 16.798 16.795 16.839 16.754 16.401 16.328 16.441 16.612 16.615 16.682 16.691 16.800 16.815 16.823 16.841 16.873 16.865 16.675 17.080 17.339 17.063 17.562 17.184 16.887 17.024 17.313 17.435 17.485 17.495 17.438 16.976 16.978 17.152 17.270 17.370 17.450 17.486 17.649 17.243 17.132 16.937 16.978 17.127 17.292 17.424 17.471 17.495 17.645 17.298 16.966 16.943 17.245 17.369 17.450 17.483 17.734 17.471 16.993 16.872 17.083 17.258 17.364 17.581 17.622 17.620 17.448 17.432 17.644 17.566 17.377 17.327 17.253 17.247 17.306 17.290 17.392 17.365 17.373 17.406 17.429 17.448 17.312 17.368 17.367 17.379 17.392 17.419 17.448 17.464 17.502 17.524 17.404 17.408 17.432 17.444 17.488 17.538 17.553 17.573 17.501 17.477 17.475 17.523 17.553 17.589 115 Table A6 (cont’d). N GC 6441: Photometry of the Variable Stars (V) HJ D 2450000 V47 V48 V49 V50 V51 V52 V53 V54 959.663 959.731 960.667 961.831 961.863 962.584 962.630 962.670 962.752 962.789 962.823 962.861 965.590 965.626 965.674 965.712 965.744 965.776 965.809 965.842 966.575 966.607 966.615 966.647 966.684 966.716 966.761 966.797 966.823 966.856 967.578 967.610 967.642 967.684 967.756 967.787 967.823 967.857 968.570 968.603 968.644 968.676 968.725 968.770 968.803 16.409 16.382 16.406 16.390 16.387 16.480 16.486 16.403 16.382 16.379 16.377 16.442 16.401 16.339 16.417 16.433 16.673 17.481 17.156 16.601 16.417 16.398 16.373 16.339 16.346 16.359 16.377 16.394 16.467 16.522 16.480 16.416 16.409 16.385 16.389 16.404 16.431 16.509 16.967 17.509 16.678 16.372 16.348 16.348 15.643 15.451 15.583 15.382 15.415 15.555 15.619 15.596 15.413 15.384 15.386 15.433 15.567 15.671 15.574 15.522 15.455 15.401 15.381 15.399 15.521 15.590 15.602 15.624 15.574 15.501 15.423 15.407 15.392 15.414 15.545 15.629 15.688 15.623 15.432 15.380 15.382 15.402 15.504 15.573 15.620 15.604 15.487 15.418 15.383 16.982 16.911 16.990 16.645 16.649 16.778 16.886 16.959 16.898 16.732 16.673 16.644 16.735 16.827 16.943 16.996 16.976 16.878 16.732 16.675 16.706 16.749 16.771 16.862 16.943 16.983 16.944 16.808 16.697 16.649 16.681 16.742 16.826 16.932 16.975 16.858 16.708 16.656 16.688 16.726 16.826 16.927 16.999 16.965 16.835 18.344 18.011 18.063 18.083 18.040 19.191 18.559 18.035 18.033 18.088 18.306 18.041 18.060 18.026 18.509 18.237 18.122 18.023 18.057 18.536 18.303 18.247 18.088 18.026 18.086 18.298 18.531 18.325 18.132 18.077 18.170 18.428 18.358 17.999 18.038 18.155 18.466 18.166 18.016 18.003 18.033 18.394 18.309 18.063 17.315 17.297 17.781 17.290 17.278 17.409 17.489 17.607 17.725 17.769 17.822 17.654 17.693 18.194 17.864 17.894 17.904 17.948 17.998 18.013 18.092 18.089 18.168 18.194 18.163 17.670 17.320 17.189 17.262 17.289 17.363 17.449 17.517 17.645 17.738 17.813 17.859 17.884 17.858 17.904 17.901 18.027 18.078 18.152 17.570 17.543 17.458 17.399 17.424 17.357 17.366 17.374 17.411 17.441 17.452 17.486 17.577 17.583 17.439 17.587 17.532 17.520 17.462 17.435 17.576 17.560 17.549 17.504 17 .439 17.414 17.373 17.362 17.350 17.343 17.432 17.388 17.358 17.330 17.337 17.358 17.375 17.391 17.364 17.334 17.365 17.366 17.378 17.402 17.408 17.612 17.497 17.401 17.423 17.334 17.367 17.395 17.415 17.478 17.476 17.489 17.640 17.624 17.308 17.470 17.401 17.394 17.349 17.311 17.439 17.416 17.421 17.366 17.308 17.283 17.267 17.316 17.328 17.350 17.294 17.296 17.290 17.327 17.351 17.414 17.434 17.451 17.367 17.338 17.385 17.390 17.420 17.461 17.451 16.747 16.664 16.545 16.427 16.476 16.636 16.677 16.705 16.740 16.736 16.696 16.566 16.507 16.545 16.232 16.646 16.676 16.703 16.718 16.719 16.630 16.465 16.432 16.288 16.232 16.268 16.353 16.427 16.471 16.517 16.680 16.697 16.718 16.724 16.722 16.692 16.577 16.412 16.294 16.344 16.420 16.470 16.541 16.607 16.653 116 Table A.6 (cont’d). NGC 6441: Photometry of the Variable Stars (V) HJ D 2450000 V55 V56 V57 V58 V59 V60 V61 V62 959.663 959.731 960.667 961.831 961.863 962.584 962.630 962.670 962.752 962.789 962.823 962.861 965.590 965.626 965.674 965.712 965.744 965.776 965.809 965.842 966.575 966.607 966.615 966.647 966.684 966.716 966.761 966.797 966.823 966.856 967.578 967.610 967.642 967.684 967.756 967.787 967.823 967.857 968.570 968.603 968.644 968.676 968.725 968.770 968.803 17.134 17.339 17.672 17.433 17.458 17.552 17.679 17.708 17.774 17.918 17.799 17.822 17.197 17.999 18.045 17.936 17.737 17.411 17.019 17.076 17.083 17.127 17.197 17.274 17.400 17.457 17.483 17.527 17.643 17.701 17.720 17.713 17.853 17.882 17.930 17.942 17.973 17.716 17.248 17.001 17.136 17.283 17.178 16.304 16.403 16.326 16.453 16.556 16.541 16.547 16.555 16.506 16.574 16.615 16.602 16.605 16.481 16.540 16.516 16.541 16.529 16.493 16.621 16.630 16.583 16.580 16.481 16.493 16.472 16.395 16.401 16.420 16.573 16.514 16.488 16.450 16.446 16.446 16.460 16.450 16.374 16.359 16.343 16.239 16.317 16.322 16.378 17.431 17.593 17.797 17.629 17.672 17.775 17.647 16.803 16.860 16.958 17.064 16.976 17.049 17.577 17.233 17.234 17.329 17.405 17 .431 17.506 17.536 17.531 17.550 17.577 17.621 17.681 17.754 17.735 17.501 17.239 16.851 16.848 16.956 17.133 17.196 17.247 17.309 17.272 17.372 17.461 17.456 17.490 17.543 17.629 17.015 16.959 16.670 16.664 16.642 16.670 16.838 16.896 16.959 16.992 16.942 17.043 17.060 16.572 17.005 16.951 17.196 17.234 17.107 16.962 16.787 16.671 16.604 16.572 16.596 16.738 16.840 16.868 16.960 17.016 16.984 17.028 17.031 17.051 17.191 17.127 17.162 16.996 16.880 16.783 16.356 16.355 16.583 16.248 17.474 17.599 17.764 17.668 17.597 17.700 17.782 17.858 17.917 17.928 17.636 17.971 18.006 17.484 17.341 17.037 17.109 17.210 17.266 17.338 17.368 17.414 17.381 17.484 17.561 17.635 17.682 17.699 17.747 17.779 17.803 17.785 17.859 17.835 17.586 17.309 17.060 17 .037 17.048 17.216 17.196 17.315 17.441 17.357 16.942 16.928 16.838 16.820 16.755 16.750 16.732 16.779 16.766 16.810 16.851 16.924 16.901 16.725 16.936 16.926 16.859 16.823 16.807 16.919 16.904 16.891 16.845 16.725 16.746 16.697 16.714 16.697 16.691 16.786 16.739 16.702 16.718 16.751 16.734 16.763 16.767 16.757 16.763 16.779 16.774 16.796 16.811 16.794 17.239 17.323 17.612 17.525 17.588 17.395 17.234 17.352 17.415 17.471 17.540 17.583 17.422 17.624 17.313 17.338 17.398 17.452 17.508 17.497 17.546 17.560 17.606 17.624 17.663 17.704 17.756 17.779 17.808 17.827 17.843 17.841 17.921 18.010 17.937 17.718 17.550 17.760 17.567 17.300 17.225 17 .306 17.369 17.407 16.674 16.784 16.982 16.905 16.935 16.977 16.964 16.990 16.995 17.042 17.102 17.123 17.089 16.849 16.603 16.645 16.661 16.733 16.789 16.856 16.893 16.894 16.899 16.992 16.931 16.927 16.979 16.975 17.015 17.069 17.087 17.094 16.992 16.593 16.579 16.656 16.721 16.810 16.832 16.881 16.905 16.947 16.985 16.970 117 Table A6 (cont’d). NGC 6441: Photometry of the Variable Stars (V) HJ D 2450000 V63 V64 V65 V66 V67 V68 V69 V70 959.663 959.731 960.667 961.831 961.863 962.584 962.630 962.670 962.752 962.789 962.823 962.861 965.590 965.626 965.674 965.712 965.744 965.776 965.809 965.842 966.575 966.607 966.615 966.647 966.684 966.716 966.761 966.797 966.823 966.856 967.578 967.610 967.642 967.684 967.756 967.787 967.823 967.857 968.570 968.603 968.644 968.676 968.725 968.770 968.803 16.940 17.022 17.286 17.135 16.998 17.020 17.044 17.039 17.070 17.090 17.131 17.230 17.191 16.807 17.312 17.383 17.253 17.254 17.120 16.962 16.813 16.808 16.769 16.807 16.863 16.905 16.965 16.941 17.032 17.062 17.092 17.105 17.113 17.185 17.162 17.259 17.234 17.387 17.248 17.086 16.972 16.827 16.857 16.996 16.825 16.872 17.040 16.910 16.942 16.936 16.975 16.990 16.986 17.020 17.034 17.016 17.035 17.076 17.059 17.033 17.055 17.085 17.078 17.079 17.134 17.125 17.098 17.076 16.971 16.824 16.807 16.815 16.842 16.887 16.920 16.908 16.953 16.993 16.968 17.005 17.028 17.026 17.044 17.048 17.085 17.103 17.118 17.089 16.898 16.898 17.015 16.879 16.831 16.846 16.851 16.895 16.918 16.956 16.990 16.794 16.807 16.944 16.908 16.888 16.912 16.929 16.951 16.966 16.964 16.974 16.955 16.944 16.969 16.985 17.037 17.026 17.054 17.061 17.060 17.051 16.983 16.753 16.695 16.722 16.757 16.734 16.754 16.799 16.841 16.867 16.904 16.914 17.183 17.151 17.019 17.018 17.060 16.972 16.997 16.970 17.050 16.991 17.059 17.116 17.165 17.188 16.944 17.171 17.120 17.115 17.063 17.046 17.187 17.172 17.141 17.067 16.944 16.955 16.918 16.877 16.886 16.885 17.014 16.986 16.927 16.938 16.965 16.918 16.987 16.986 16.978 16.951 16.993 16.958 17.002 17.030 17.009 17.028 16.323 16.588 16.711 16.820 16.930 17.039 17.012 17.055 17.128 17.246 16.988 16.880 16.602 16.497 16.447 16.565 16.784 16.784 16.808 16.913 16.988 17.040 17.097 17.176 17 .171 17.186 17.238 17.227 17.296 17.108 16.392 16.519 16.639 16.745 16.828 16.157 15.945 16.103 16.330 16.224 15.986 15.966 15.992 16.247 16.246 16.272 15.930 15.961 16.320 16.195 16.222 16.386 16.364 16.200 15.896 15.991 16.000 16.110 16.320 16.386 16.420 16.378 16.224 16.113 15.963 16.052 16.216 16.276 16.290 16.224 16.056 15.987 15.973 16.230 16.242 16.269 16.059 15.966 17 .225 17.377 17.408 17.266 17.222 17.499 17.539 17.592 17.604 17.570 17.513 17.517 17.602 17.517 17.606 17.440 17.312 17.243 17.220 17 .274 17.600 17.626 17.615 17.614 17.606 17.556 17.467 17.513 17.450 17.356 17.393 17.451 17.482 17.548 17.619 17.623 17.587 17.533 17.321 17.243 17.283 17.325 17.436 17.516 17.511 17.661 17.272 17.367 17.764 17.779 17.279 17.293 17.434 17.713 17.751 17.671 17.420 17.773 17.783 17.335 17.424 17.296 17.265 17.335 17.472 17.786 17.774 17.749 17.501 17.335 17.251 17.326 17.490 17.609 17.713 17.678 17.431 17.303 17.270 17.521 17.671 17.755 17.778 17.460 17.288 17.387 17.622 17.732 17.800 118 Table A6 (cont’d). NGC 6441: Photometry of the Variable Stars (V) HJ D 2450000 V71 V72 V73 V74 V75 V76 V77 V78 959.663 959.731 960.667 961.831 961.863 962.584 962.630 962.670 962.752 962.789 962.823 962.861 965.590 965.626 965.674 965.712 965.744 965.776 965.809 965.842 966.575 966.607 966.615 966.647 966.684 966.716 966.761 966.797 966.823 966.856 967.578 967.610 967.642 967.684 967.756 967.787 967.823 967.857 968.570 968.603 968.644 968.676 968.725 968.770 968.803 17.639 17.686 17.377 17.733 17.678 17.693 17.548 17.244 17.218 17.305 17.458 17.476 17.389 17.399 17.319 17.414 17.532 17.635 17.700 17.7 29 17.712 17.700 17.526 17.399 17.322 17.231 17.305 17.392 17.513 17.532 17.616 17.679 17.704 17.433 17.362 17.253 17.268 17.277 17.301 17.443 17.527 17.655 17.715 17.607 17.409 17.126 17.112 17.270 17.199 17.374 17.521 17.525 17.298 17.163 17.112 17.353 17.198 17.381 17.230 17.362 17.478 17.558 17.593 17.161 17.122 17.128 17.230 17.381 17.496 17.563 17.551 17.424 17.221 17.235 17.351 17.475 17.562 17.453 17.235 17.115 17.115 17.485 17.551 17.587 17.534 17.224 17.086 17.133 16.871 17.099 17.065 16.766 16.791 17.078 17.154 17.189 16.829 16.771 16.795 16.911 17.011 16.843 16.869 16.803 16.907 17.040 17.138 17.185 16.881 16.805 16.808 16.804 16.869 16.978 17.121 17.200 17.176 17.095 16.800 16.813 16.880 17.013 17.163 17.168 17.026 16.872 16.814 16.886 17.020 17.091 17.153 17.091 16.883 17.673 17.809 17.788 17.600 17.830 17.773 17.504 17.329 17.447 17.624 17.745 17.357 17.397 17.760 17.731 17.783 17.825 17.764 17.543 17.405 17.513 17.541 17.668 17.760 17.800 17.749 17.514 17.432 17.322 17.594 17.715 17.760 17.811 17.479 17.371 17.331 17.409 17.753 17.768 17.802 17.698 17.467 17.313 17.359 17.187 17 .376 17.419 17.532 17.390 17.456 17.550 17.370 17.301 17.225 17.180 17.409 17.323 17.505 17.171 17.224 17.313 17.408 17.454 17.291 17.404 17.415 17.449 17.505 17.508 17.493 17.438 17.360 17.266 17.519 17.445 17 .327 17.209 17.185 17.293 17.378 17.428 17.228 17.211 17.341 17.326 17.407 17.466 17.399 17.681 17.832 17.805 18.011 17.940 17.934 18.018 18.065 18.061 17.972 17.912 17.911 18.096 17.975 17.792 17.863 17.784 17.720 17.714 17.763 18.004 17.954 17.951 17.885 17.792 17.722 17.716 17.796 17.860 17.942 17.964 17.874 17.762 17.697 17.809 17.909 17.981 18.057 17.852 17.746 17.717 17.752 17.875 17.955 17.989 17.516 17.279 17 .650 17.694 17.689 17.790 17.687 17.507 17.224 17.253 17.380 17.537 17.738 17.696 17.669 17.418 17.262 17.238 17.314 17.440 17.411 17.510 17.528 17.616 17.669 17.697 17.651 17.525 17.449 17.325 17.469 17.317 17.219 17.302 17.567 17.635 17.689 17.720 17.759 17.773 17.664 17.543 17.374 17.227 17.276 18.043 18.143 17.856 18.091 18.100 18.027 17.761 17.596 17.724 17.877 17.991 18.079 17.878 17.995 17.985 18.073 17.999 17.771 17.701 17.561 17.635 17.718 17.755 17.871 17.985 18.056 18.076 17.964 17.811 17.736 17.630 17 .581 17.640 17.803 18.045 18.065 18.071 17.921 17.936 17 .762 17.584 17.596 17.760 17.924 18.070 119 Table A6 (cont’d). NGC 6441: Photometry of the Variable Stars (V) HJ D 2450000 V79 V80 V81 V82 V83 V84 V85 V86 959.663 959.731 960.667 961.831 961.863 962.584 962.630 962.670 962.752 962.789 962.823 962.861 965.590 965.626 965.674 965.712 965.744 965.776 965.809 965.842 966.575 966.607 966.615 966.647 966.684 966.716 966.761 966.797 966.823 966.856 967.578 967.610 967.642 967.684 967.756 967.787 967.823 967.857 968.570 968.603 968.644 968.676 968.725 968.770 968.803 17.242 17.276 16.965 17.168 17.384 17.443 17.386 17.172 17.016 17.037 17.149 17.348 17.205 17.295 16.971 16.989 17.081 17.214 17.362 17.065 17.096 17.120 17.263 17.295 17.441 17.487 17.435 17.434 17.305 17.512 17.489 17.474 17.377 17.165 17.028 16.983 17.134 17.148 17.028 17.019 16.946 17.100 17.250 17.193 17.396 17.591 17.653 17.261 17.303 17.409 17.290 17.253 17.279 17.334 17.410 17.511 17.582 17.580 17.299 17.451 17.378 17.321 17.281 17.254 17.571 17.478 17.462 17.377 17.299 17.274 17.240 17.279 17.302 17.354 17.337 17.291 17.255 17.249 17.349 17.433 17.542 17.623 17.305 17.306 17.340 17.409 17.557 17.629 17.626 17.765 17.748 17.839 17.763 17.878 17.817 17.766 17.759 17.817 17.834 17.928 17.854 17.806 17.888 17.758 17.768 17.804 17.864 17.951 17.779 17.796 17.805 17.837 17.888 18.005 18.054 18.058 17.973 17.889 18.054 18.101 18.056 17.936 17.791 17.793 17.750 17.761 17.880 17.809 17.767 17.740 17.747 17.767 17.829 16.460 16.406 16.639 16.481 16.524 16.469 16.437 16.409 16.480 16.514 16.602 16.519 16.477 16.587 16.426 16.435 16.477 16.543 16.602 16.601 16.656 16.660 16.646 16.587 16.520 16.447 16.418 16.425 16.419 16.434 16.440 16.467 16.498 16.561 16.551 16.496 16.460 16.533 16.444 16.419 16.406 16.421 16.468 16.543 17.596 17.771 17.701 17.577 17.620 17.734 17.604 17.536 17.542 17.617 17.731 17.789 17.634 17.691 17.569 17.659 17.587 17.552 17.520 17.537 17.803 17.779 17.783 17.682 17.569 17.521 17.494 17.546 17.579 17.668 17.675 17.602 17.543 17.507 17.604 17.673 17.764 17.756 17.602 17.563 17.563 17.573 17.657 17.700 17.687 17.493 17.197 17.317 17.525 17.395 17.245 17.227 17.551 17.570 17.581 17.411 17.545 17.594 17.226 17.415 17.238 17.133 17.203 17.393 17.646 17.609 17.552 17.342 17.226 17.149 17.154 17.280 17.397 17.535 17.521 17.305 17.165 17.171 17.447 17.442 17.560 17.598 17.363 17.218 17.238 17.373 17.526 17.587 17.595 17.589 17.706 17.624 17.877 17.685 17.537 17.541 17.812 17.495 17.613 17.753 17.577 17.572 17.706 17.589 17.518 17.551 17.817 17.748 17.573 17.508 17.659 17.714 17.835 17.589 17.529 17.687 17.752 17.569 17.508 17.577 17.713 17.752 17.513 17.755 17.763 17.576 17.537 17.525 17.732 17.695 17.505 17.562 17.734 17.538 18.154 17.787 17.871 17.891 18.127 17.815 17.804 18.011 17.827 17.786 17.958 17.853 18.020 17.825 17.847 17.836 17.949 18.253 18.013 17.832 18.080 18.143 18.042 17.825 17.806 18.047 18.240 17.943 17.805 18.071 18.104 17.886 17.787 18.220 18.014 17.828 17.786 18.214 17.945 17.808 17.803 18.185 17.934 17.774 120 Table A6 (cont’d). NGC 6441: Photometry of the Variable Stars (V) HJ D 2450000 V87 V88 V89 V90 V91 V92 V93 V94 959.663 959.731 960.667 961.831 961.863 962.584 962.630 962.670 962.752 962.789 962.823 962.861 965.590 965.626 965.674 965.712 965.744 965.776 965.809 965.842 966.575 966.607 966.615 966.647 966.684 966.716 966.761 966.797 966.823 966.856 967.578 967.610 967.642 967.684 967.756 967.787 967.823 967.857 968.570 968.603 968.644 968.676 968.725 968.770 968.803 17.247 17.076 17.087 17.120 17.218 17.156 17.228 17.099 17.083 17.215 17.241 17.127 17.215 17.096 17.219 17.085 17.217 17.244 17.147 17.074 17.099 17.093 17.096 17.159 17.219 17.146 17.025 17.038 17.113 17.223 17.184 17.265 17.190 17.079 17.147 17.211 17.158 17.062 17.140 17.042 17.028 17.133 17.253 17.138 17.092 17.550 17.831 17.938 17.636 17.536 17.613 17.806 17.667 17.552 17.518 17.593 17.696 17.897 17.558 17.612 17.528 17.526 17.644 17.822 17.836 17.675 17.649 17.543 17.558 17.661 17.932 17.888 17.700 17.600 17.549 17.622 17.761 17.957 17.587 17.544 17.581 17.692 17.978 17.918 17.631 17.556 17.565 17 .724 17.937 18.454 18.417 18.480 18.614 18.639 18.410 18.373 18.544 18.587 18.508 18.428 18.433 18.363 18.625 18.580 18.674 18.617 18.466 18.406 18.415 18.477 18.526 18.666 18.625 18.478 18.367 18.330 18.401 18.532 18.674 18.550 18.454 18.354 18.475 18.593 18.593 18.472 18.437 18.334 18.424 18.489 18.566 18.445 18.438 18.405 18.464 18.544 18.410 18.409 18.429 18.452 18.527 18.698 18.659 18.542 18.419 18.579 18.674 18.589 18.622 18.485 18.412 18.394 18.378 18.433 18.432 18.467 18.490 18.589 18.636 18.609 18.600 18.508 18.446 18.467 18.436 18.374 18.389 18.552 18.637 18.685 18.675 18.740 18.663 18.508 18.447 18.400 18.447 18.523 19.439 19.789 19.976 19.585 19.315 19.334 19.471 19.611 19.399 19.285 19.276 19.371 19.473 19.325 19.794 19.474 19.326 19.299 19.372 19.772 19.986 19.889 19.526 19.325 19.278 19.404 19.671 19.850 19.678 19.409 19.287 19.320 19.491 19.747 19.448 19.349 19.266 19.539 19.614 19.926 19.634 19.425 19.287 19.312 18.457 18.475 18.752 18.793 18.783 18.520 18.526 18.652 18.599 18.492 18.473 18.493 18.757 18.637 18.585 18.473 18.461 18.512 18.602 18.701 18.491 18.486 18.457 18.497 18.585 18.673 18.636 18.553 18.497 18.442 18.808 18.825 18.631 18.521 18.444 18.469 18.548 18.672 18.500 18.470 18.514 18.581 18.792 18.765 18.609 17.368 17.112 17.362 17.428 17.528 17.533 17.461 17.115 17.099 17.147 17.294 17.432 17.497 17.513 17.558 17.417 17.222 17.112 17.094 17.291 17.384 17.440 17.477 17.513 17.511 17.387 17.197 17.081 17.017 17.221 17.314 17.407 17.492 17.482 17.344 17.187 17.095 17.208 17.234 17.369 17.507 17.527 17.520 17.416 17.570 17.410 17.161 17.357 17.228 17.303 17.425 17.534 17.511 17.388 17.339 17.272 17.217 17.344 17.374 17.434 17.472 17.554 17.561 17.565 17.620 17.606 17.479 17.344 17.299 17.187 17.197 17.205 17.283 17.212 17.251 17.344 17.449 17.549 17.530 17.437 17.341 17.554 17.409 17.316 17.213 17.190 17.257 17.245 121 Table A6 (cont’d). NGC 6441: Photometry of the Variable Stars (V) HJ D 2450000 V95 V96 V97 V98 V99 V100 V101 V102 959.663 959.731 960.667 961.831 961.863 962.584 962.630 962.670 962.752 962.789 962.823 962.861 965.590 965.626 965.674 965.712 965.744 965.776 965.809 965.842 966.575 966.607 966.615 966.647 966.684 966.716 966.761 966.797 966.823 966.856 967.578 967.610 967.642 967.684 967.756 967.787 967.823 967.857 968.570 968.603 968.644 968.676 968.725 968.770 968.803 17.691 17.430 17.824 17.685 17.565 17.715 17.592 17.792 17.465 17.730 17.409 17.644 17.803 17.696 17.794 17.444 17.652 17.789 17.380 17.599 17.851 17.860 17.320 17.696 17.669 17.635 17.837 17.271 17.695 17.736 17.790 17.392 17.768 17.687 17.781 17.433 17.713 17.758 17.769 17.556 17.816 17.427 17.797 17.454 17.628 17.608 17.578 17.734 17.785 17.657 17.709 17.701 17.723 17.741 17.703 17.718 17.691 17.632 17.582 17.610 17.575 17.601 17.603 17.609 17.599 17.598 17.611 17.602 17.582 17.609 17.626 17.651 17.654 17.669 17.626 17.637 17.628 17.658 17.672 17.702 17.711 17.717 17.685 17.694 17.657 17.681 17.688 17.727 17.404 17.354 17.326 17.475 17.445 17.505 17.489 17.507 17.536 17.534 17.545 17.533 17.492 17.385 17.393 17.355 17.360 17.387 17.402 17.426 17.398 17.408 17.395 17.385 17.405 17.431 17.416 17.454 17.439 17.431 17.430 17.432 17.444 17.463 17.501 17.503 17.501 17.424 17.436 17.498 17.434 17 .468 17.514 17.466 14.800 14.801 14.782 14.762 14.766 14.728 17.741 14.765 14.772 14.773 14.764 14.773 14.645 14.665 14.646 14.655 14.654 14.657 14.666 14.660 14.638 14.624 14.626 14.638 14.646 14.629 14.643 14.619 14.624 14.621 14.619 14.619 14.629 14.624 14.610 14.614 14.605 14.626 14.563 14.561 14.583 14.566 14.573 14.568 14.558 16.262 16.258 16.285 16.329 16.336 16.339 16.366 16.369 16.378 16.376 16.375 16.364 16.452 16.457 16.504 16.452 16.463 16.471 16.479 16.471 16.478 16.478 16.491 16.486 16.504 16.509 16.504 16.529 16.516 16.506 16.510 16.520 16.526 16.536 16.533 16.540 16.542 16.539 16.530 16.527 16.552 16.552 16.559 16.570 16.564 16.922 16.882 16.903 16.888 16.907 17.851 17.807 17.645 17.252 17.132 17.036 16.985 16.897 16.876 16.865 16.887 16.858 16.852 16.871 16.865 16.886 16.853 16.869 16.857 16.865 16.872 16.860 16.860 16.880 16.891 17.877 17.839 17.716 17.479 17.181 17.088 16.993 16.969 16.903 16.855 16.853 16.860 16.855 16.830 16.846 18.263 18.224 18.104 18.075 18.096 18.085 18.118 18.130 18.108 18.155 18.128 18.121 18.153 18.126 18.266 18.090 18.078 18.096 18.129 18.102 18.156 18.198 18.202 18.194 18.266 18.284 18.292 18.361 18.296 18.305 18.119 18.125 18.112 18.102 18.105 18.145 18.139 18.139 19.747 19.749 19.875 19.444 18.899 18.585 18.355 15.786 15.844 15.842 15.837 15.874 15.858 15.805 15.790 15.812 15.846 15.877 15.872 15.890 15.780 15.890 15.832 15.810 15.789 15.793 15.870 15.891 15.887 15.857 15.780 15.770 15.769 15.813 15.826 15.844 15.849 15.802 15.769 15.781 15.835 15.851 15.867 15.860 15.800 15.768 15.806 15.812 15.855 15.863 15.848 122 Table A6 (cont’d). NGC 6441: Photometry of the Variable Stars (V) HJ D 2450000 V103 V104 SV10 SV11 SV12 SV13 SV14 SV15 959.663 959.731 960.667 961.831 961.863 962.584 962.630 962.670 962.752 962.789 962.823 962.861 965.590 965.626 965.674 965.712 965.744 965.776 965.809 965.842 966.575 966.607 966.615 966.647 966.684 966.716 966.761 966.797 966.823 966.856 967.578 967.610 967.642 967.684 967.756 967.787 967.823 967.857 968.570 968.603 968.644 968.676 968.725 968.770 968.803 18.373 18.464 18.386 18.333 18.358 18.343 18.423 18.543 18.527 18.455 18.381 18.348 18.330 18.370 18.376 18.411 18.468 18.476 18.418 18.391 18.340 18.327 18.333 18.370 18.419 18.512 18.574 18.542 18.469 18.410 18.338 18.297 18.328 18.393 18.469 18.470 18.420 18.438 18.343 18.330 18.394 18.410 18.507 18.517 19.320 19.042 19.479 19.360 19.733 19.362 19.250 19.124 19.218 19.275 19.455 19.211 19.257 19.393 19.165 19.110 19.269 19.607 19.813 19.945 19.896 19.590 19.459 19.393 19.360 19.260 19.176 19.262 19.316 19.305 19.346 19.580 19.897 19.385 19.309 19.181 19.176 19.233 19.363 19.183 19.261 19.610 20.185 20.141 17.742 17.651 17.678 17.609 17.654 17.627 17.654 17.697 17.622 17.624 17.654 17.705 17.632 17.644 17.627 17.698 17.641 17.614 17.631 17.679 17.667 17.690 17.703 17.684 17.627 17.613 17.653 17.690 17.707 17.651 17.708 17.658 17.617 17.615 17.690 17.664 17.627 17.624 17.654 17.614 17.660 17.715 17.680 17.616 17.618 17.693 17.726 17.740 17.777 17.754 17.752 17.669 17.670 17.758 17.786 17.752 17.689 17.779 17.780 17.640 17.661 17.634 17.660 17.692 17.724 17.789 17.757 17.732 17.670 17.640 17.648 17.692 17.729 17.710 17.699 17.716 17.663 17.636 17.664 17.711 17.702 17.666 17.665 17.669 17.654 17.698 17.695 17.710 17 .664 17 .653 17.643 17.603 17.605 17 .535 17.531 17.515 17.514 17.495 17.517 17.513 17.532 17.602 17.597 17.617 17.613 17.626 17.617 17.609 17.604 17.616 17.645 17.621 17.608 17.617 17.617 17.593 17.619 17.586 17.561 17.636 17.616 17.593 17.578 17 .537 17.545 17.536 17.522 17.569 17.568 17.529 17.523 17.509 17.482 17.493 16.532 16.523 16.513 16.557 16.566 16.606 16.606 16.616 16.616 16.627 16.619 16.629 16.587 16.581 16.491 16.572 16.567 16.564 16.565 16.560 16.501 16.485 16.494 16.492 16.491 16.489 16.479 16.494 16.490 16.492 16.466 16.467 16.464 16.461 16.463 16.476 16.475 16.468 16.514 16.494 16.503 16.495 16.501 16.501 16.505 17.474 17.514 17.318 17.433 17.319 17.241 17.252 17.162 17.306 17.358 17.299 17.291 17.278 17.215 17.394 17.438 17.501 17.405 17.375 17.306 17.237 17.333 17.239 17.215 17.262 17.313 17.504 17.461 17.433 17.385 17.363 17.332 17.293 17.212 17.294 17.368 17.381 17.371 17.338 17.310 17.366 17.268 17.268 17.404 16.737 16.795 16.558 16.698 16.877 16.999 16.909 16.918 16.870 16.857 16.881 16.852 16.869 16.643 16.860 16.825 16.937 16.941 16.936 16.873 16.809 16.801 16.738 16.643 16.706 16.726 16.777 16.775 16.805 16.983 16.958 16.912 16.940 16.888 16.807 16.760 16.721 16.649 16.655 16.780 16.662 16.693 16.830 16.635 123 Table A7 NGC 6441: Photometry of the Variable Stars (B) HJ D 2450000 V1 V2 V5 V6 V9 V10 V37 V38 959.648 960.649 961.820 961.852 962.588 962.635 962.674 962.741 962.778 962.812 962.848 965.595 965.631 965.662 965.701 965.733 965.764 965.798 965.831 966.579 966.619 966.652 966.688 966.720 966.750 966.783 966.812 966.845 967.567 967.599 967.631 967.672 967.705 967.760 967.792 967.827 967.862 968.573 968.607 968.648 968.680 968.714 968.758 968.792 18.716 18.792 18.861 18.876 18.929 18.922 18.929 18.94 18.958 18.925 18.956 19.053 19.096 19.091 19.08 19.062 19.122 18.963 19.083 19.118 19.15 19.126 19.119 19.157 19.107 19.168 19.138 19.131 19.122 19.171 19.17 19.193 19.199 19.166 19.195 19.215 19.213 19.194 19.202 19.205 19.19 19.215 19.251 19.235 18.462 17.934 18.001 18.111 18.035 18.299 18.45 18.431 18.25 18.149 18.026 17.92 17.976 18.097 18.265 18.364 18.442 18.477 18.486 18.502 18.33 18.123 18.057 17.948 17.928 17.953 18.039 17.946 18.004 18.142 18.27 18.385 18.477 18.416 18.216 18.15 18.362 18.224 18.07 17.98 17.943 18.049 18.183 17.291 17.205 17.163 17.16 17.092 17.109 17.127 17.126 17.13 17.113 17.118 16.991 17.023 17.016 17.005 17.006 17.012 17.013 17.008 16.966 16.98 16.981 16.998 16.994 16.995 16.999 16.987 16.993 16.946 16.959 16.954 16.966 16.967 16.958 16.977 16.968 16.964 16.947 16.914 16.935 16.952 16.943 16.944 16.964 15.507 15.504 15.69 15.671 15.741 15.772 15.772 15.781 15.783 15.786 16.274 16.284 16.302 16.291 16.311 16.302 16.3 16.3 16.433 16.475 16.469 16.475 16.491 16.484 16.494 16.488 16.498 16.583 16.595 16.605 16.608 16.622 16.597 16.619 16.621 16.601 16.732 16.71 16.722 16.718 16.721 16.718 16.725 17.221 17.148 17.127 17.171 17.04 17.056 17.092 17.11 17.1 17.145 16.905 16.894 16.927 16.923 16.944 16.938 16.966 16.976 16.833 16.839 16.879 16.891 16.899 16.915 16.894 16.908 16.916 16.778 16.813 16.852 16.862 16.867 16.895 16.889 16.884 16.916 16.748 16.79 16.815 16.857 16.874 16.907 16.87 19.349 19.365 19.351 19.329 19.32 19.319 19.334 19.364 19.362 19.303 19.344 19.202 19.236 19.242 19.279 19.273 19.24 19.229 19.217 19.152 19.202 19.223 19.195 19.206 19.219 19.202 19.204 19.219 19.095 19.157 19.196 19.214 19.168 19.179 19.19 19.159 19.214 19.175 19.084 19.103 19.149 19.127 19.135 19.144 17.724 18.908 18.818 18.893 19.038 17.508 17.869 18.088 18.257 18.4 19.017 19.042 18.933 18.126 17.503 17.626 17.818 18.037 18.535 18.594 18.663 18.819 18.834 18.818 18.925 18.977 19.047 17.537 17.623 17.791 18.028 18.204 18.371 18.459 18.535 18.622 18.814 18.879 19.006 19.085 19.005 18.293 17 .516 17.998 18.604 17.907 17.973 18.02 18.21 18.36 18.436 18.474 18.541 18.199 18.262 18.332 18.409 18.482 18.544 18.533 18.585 18.617 18.665 18.714 18.738 18.813 18.807 18.72 18.383 18.158 18.234 17.942 17.745 17.806 17.93 18.061 18.163 18.226 18.325 18.292 18.341 18.411 18.488 18.556 18.569 18.633 124 Table A.7 (cont’d). NGC 6441: Photometry of the Variable Stars (B) HJ D 2450000 V39 V40 V41 V42 V43 V44 V45 V46 959.648 960.649 961.820 961.852 962.588 962.635 962.674 962.741 962.778 962.812 962.848 965.595 965.631 965.662 965.701 965.733 965.764 965.798 965.831 966.579 966.619 966.652 966.688 966.720 966.750 966.783 966.812 966.845 967.567 967.599 967.631 967.672 967.705 967.760 967.792 967.827 967.862 968.573 968.607 968.648 968.680 968.714 968.758 968.792 18.825 18.229 18.328 18.189 18.224 18.304 18.459 18.529 18.617 18.696 18.983 19.051 19.101 19.096 19.100 19.028 18.763 18.552 19.096 18.915 18.541 18.420 18.189 18.131 18.160 18.221 18.306 18.173 18.158 18.234 18.322 18.396 18.521 18.562 18.635 18.694 18.491 18.515 18.601 18.657 18.747 18.763 18.835 18.920 18.393 17.961 18.094 18.372 18.619 18.642 18.729 18.776 18.865 17.466 17.572 17.740 17.923 18.075 18.197 18.273 18.342 18.675 18.695 18.696 18.776 18.848 18.863 18.927 18.801 18.248 17.550 17.720 17.874 18.033 18.181 18.304 18.400 18.485 18.614 18.672 18.697 18.808 18.866 18.857 18.746 18.164 18.075 18.008 18.038 18.079 18.050 18.091 18.131 18.177 18.217 18.249 18.245 18.065 18.110 18.135 18.166 18.156 18.215 18.233 18.241 18.225 18.099 17.873 17.614 17.512 17.545 17.633 17.680 17.752 17.709 17.779 17.826 17.898 17.939 18.001 18.039 18.069 18.111 18.030 18.052 18.102 18.143 18.167 18.181 18.206 18.317 18.478 18.273 18.105 18.450 18.032 17.964 18.033 18.110 18.206 18.660 18.669 18.684 18.700 18.757 18.781 18.702 18.535 18.750 18.681 18.447 18.292 18.137 17.994 17.956 17.996 18.065 18.014 17.986 18.017 18.069 18.151 18.250 18.354 18.393 18.436 18.319 18.307 18.414 18.425 18.463 18.515 18.561 18.677 18.572 18.501 18.554 18.560 18.563 18.595 18.668 18.709 18.724 18.800 18.384 18.430 18.468 18.500 18.576 18.606 18.597 18.667 18.650 18.714 18.701 18.714 18.786 18.794 18.774 18.679 18.388 18.765 18.632 18.334 18.161 17.989 18.023 18.086 18.178 18.251 18.136 18.202 18.293 18.361 18.447 18.471 18.535 18.064 18.077 17.992 18.036 18.181 18.216 18.222 17.226 17.244 17.397 17.567 18.119 18.179 18.191 18.215 18.136 17.719 17.179 17.299 17.839 17.906 17.955 17.986 18.059 18.127 18.138 18.136 18.161 18.080 17.550 17.220 17.365 17.514 17.739 17.805 17.902 17.945 18.113 18.118 18.100 18.163 18.162 18.179 17.961 17.732 17.678 18.428 18.488 17.768 17.769 18.120 18.276 18.361 18.420 18.061 17.608 17.620 17.834 18.053 18.195 18.299 18.388 18.451 17.722 17.568 17.688 17.922 18.068 18.240 18.328 18.398 18.584 18.234 17.693 17.561 17.761 18.096 18.241 18.347 18.417 18.611 18.221 17.599 17.593 17.780 18.042 18.210 18.557 18.371 18.308 18.630 18.489 18.272 18.209 18.123 18.093 18.162 18.185 18.243 18.254 18.280 18.343 18.364 18.402 18.217 18.317 18.327 18.341 18.390 18.408 18.537 18.468 18.523 18.350 18.363 18.410 18.394 18.463 18.479 18.537 18.573 18.603 18.435 18.530 18.488 18.524 18.605 125 Table A.7 (cont’d). NGC 6441: Photometry of the Variable Stars (B) HJ D 2450000 V47 V48 V49 V50 V51 V52 V53 V54 959.648 960.649 961.820 961.852 962.588 962.635 962.674 962.741 962.778 962.812 962.848 965.595 965.631 965.662 965.701 965.733 965.764 965.798 965.831 966.579 966.619 966.652 966.688 966.720 966.750 966.783 966.812 966.845 967.567 967.599 967.631 967.672 967.705 967.760 967.792 967.827 967.862 968.573 968.607 968.648 968.680 968.714 968.758 968.792 17.375 17.420 17.373 17.385 17.381 17.454 17.469 17.396 17.394 17.378 17.355 17.427 17.398 17.398 17.392 17.416 17.566 18.296 18.439 17.521 17.382 17.367 17.343 17.350 17.364 17.381 17.405 17.445 17.482 17.492 17.440 17.410 17.406 17.380 17.392 17.402 17.461 17.541 18.213 18.290 17.611 17.373 17.365 17.347 16.562 16.473 16.259 16.282 16.471 16.502 16.464 16.318 16.284 16.284 16.316 16.482 16.572 16.555 16.431 16.346 16.302 16.268 16.285 16.418 16.488 16.499 16.444 16.365 16.325 16.287 16.278 16.305 16.427 16.509 16.572 16.531 16.425 16.300 16.267 16.267 16.319 16.394 16.462 16.499 16.473 16.390 16.335 16.284 17.738 17.755 17.349 17.327 17.533 17.679 17.770 17.700 17.489 17.377 17.342 17.469 17.605 17.711 17.784 17.780 17.680 17.480 17.398 17.425 17.541 17.652 17.764 17.788 17.762 17.605 17.431 17.365 17.389 17.451 17.540 17.712 17.784 17.747 17.571 17.399 17.354 17.385 17.441 17.605 17.738 17.804 17.791 17.622 19.671 19.180 19.629 19.291 19.226 19.430 19.780 19.247 19.147 19.220 19.353 19.207 19.257 19.415 19.750 19.517 19.262 19.202 19.161 19.707 19.367 19.199 19.195 19.241 19.420 19.681 19.528 19.249 19.259 19.280 19.511 19.599 19.324 19.139 19.216 19.353 19.699 19.218 19.196 19.082 19.224 19.463 19.510 19.316 18.278 18.739 17.917 17.982 18.048 18.274 18.393 18.561 18.654 18.756 18.875 18.614 18.698 18.785 18.860 18.941 18.922 18.962 19.043 19.107 19.184 19.249 19.232 19.156 18.728 18.270 17.890 17.972 18.025 18.156 18.271 18.388 18.489 18.600 18.749 18.823 18.895 18.966 18.909 19.005 19.032 19.093 19.178 19.279 18.591 18.418 18.352 18.362 18.276 18.324 18.357 18.408 18.415 18.491 18.575 18.575 18.591 18.544 18.529 18.493 18.418 18.390 18.533 18.515 18.445 18.375 18.334 18.309 18.274 18.264 18.271 18.391 18.324 18.298 18.236 18.250 18.274 18.285 18.327 18.369 18.299 18.281 18.294 18.366 18.351 18.380 18.432 18.551 18.320 18.323 18.334 18.245 18.324 18.381 18.404 18.434 18.459 18.624 18.560 18.511 18.385 18.305 18.289 18.190 18.133 18.309 18.259 18.199 18.133 18.131 18.130 18.172 18.174 18.250 18.153 18.129 18.176 18.189 18.215 18.294 18.334 18.363 18.406 18.285 18.288 18.360 18.386 18.380 18.420 18.459 17.751 17.464 17.332 17.408 17.615 17.698 17.726 17.727 17.726 17.705 17.558 17.471 17.543 17.600 17.643 17.689 17.705 17.732 17.725 17.530 17.294 17.116 17.066 17.148 17.223 17.337 17.390 17.483 17.695 17.713 17.728 17.723 17.730 17.713 17.671 17.468 17.253 17.164 17.262 17.351 17.431 17.507 17.586 17.665 126 Table A.7 (cont’d). NGC 6441: Photometry of the Variable Stars (B) HJ D 2450000 V55 V56 V57 V58 V59 V60 V61 V62 959.648 960.649 961.820 961.852 962.588 962.635 962.674 962.741 962.778 962.812 962.848 965.595 965.631 965.662 965.701 965.733 965.764 965.798 965.831 966.579 966.619 966.652 966.688 966.720 966.750 966.783 966.812 966.845 967.567 967.599 967.631 967.672 967.705 967.760 967.792 967.827 967.862 968.573 968.607 968.648 968.680 968.714 968.758 968.792 17.649 18.444 17.996 18.018 18.160 18.271 18.381 18.421 18.536 18.568 18.649 18.591 18.649 18.689 18.793 18.750 18.776 18.612 18.164 17.525 17.649 17.782 17.919 17.999 18.065 18.183 18.242 18.363 18.447 18.543 18.539 18.491 18.546 18.689 18.776 18.810 18.781 18.615 18.264 17.682 17.536 17.643 17.820 17.937 17.349 17.800 17.634 17.634 17.683 17.713 17.765 17.825 17.828 17.909 17.861 17.910 17.921 17 .876 17.828 17.746 17.619 17.520 17.879 17.828 17.624 17.581 17.434 17 .313 17.280 17.316 17.773 17.625 17.570 17.343 17.278 17.306 17.373 17.431 17.477 17.367 17.285 17.247 17.368 17.367 17.444 17.490 18.535 17.724 18.628 18.696 18.739 18.564 17.510 17.496 17.617 17.786 17.709 17.828 17.971 18.066 18.170 18.196 18.294 18.398 18.476 18.524 18.539 18.597 18.679 18.662 18.751 18.730 18.540 18.091 17.588 17.490 17.638 17.759 17.952 18.069 18.155 18.254 18.373 18.418 18.508 18.572 18.588 18.636 18.679 17.883 17.554 17.364 17.270 17.514 17.622 17.745 17.792 17.856 17.889 17.895 17.954 17.943 17.989 17.922 17.983 17.967 18.036 17 .734 17.336 17.277 17.357 17 .453 17.557 17.656 17.675 17.645 17.858 17.916 17.920 17.974 17 .943 17.950 17.979 17.920 17.997 17.964 17.857 17.631 17.347 17.350 17.431 17.449 18.290 18.484 18.518 18.558 18.691 18.774 18.844 18.849 18.621 18.858 18.884 18.605 18.125 17.640 17.632 17.773 17.905 18.043 18.155 18.247 18.327 18.437 18.503 18.568 18.585 18.640 18.637 18.695 18.767 18.790 18.865 18.699 18.212 17.842 17.629 17.650 17.743 17.885 18.007 18.084 18.188 18.278 18.074 17.878 17.915 17.828 17.832 17.880 17.903 17.955 17.966 18.020 18.071 18.107 18.091 18.093 18.073 18.024 17.968 17.937 18.084 18.028 17.950 17.877 17.854 17.820 17.819 17.801 17.807 17.890 17.835 17.800 17.916 17.821 17.852 17.887 17.910 17.931 17.799 17.813 17.863 17.916 17.896 17.948 17.970 18.020 18.541 18.660 18.430 18.478 18.127 17.993 18.151 18.270 18.362 18.464 18.425 18.150 17.983 18.054 18.157 18.229 18.311 18.400 18.423 18.507 18.548 18.632 18.704 18.715 18.753 18.801 18.837 18.822 18.880 18.910 18.943 19.000 19.047 18.966 18.520 18.380 18.611 18.394 18.028 18.027 18.093 18.212 18.330 17.538 17.932 17.988 18.168 18.257 18.286 18.340 18.421 18.406 18.427 18.300 17.907 17.440 17.428 17.538 17.665 17.786 17.954 18.052 18.101 18.164 18.232 18.263 18.255 18.271 18.319 18.367 18.457 18.413 18.315 17.915 17.390 17.499 17.627 17.740 17.858 17.893 17.995 18.046 18.109 18.205 18.242 127 Table A.7 (cont’d). NGC 6441: Photometry of the Variable Stars (B) HJ D 2450000 V63 V64 V65 V66 V67 V68 V69 V70 959.648 960.649 961.820 961.852 962.588 962.635 962.674 962.741 962.778 962.812 962.848 965.595 965.631 965.662 965.701 965.733 965.764 965.798 965.831 966.579 966.619 966.652 966.688 966.720 966.750 966.783 966.812 966.845 967.567 967.599 967.631 967.672 967.705 967.760 967.792 967 .827 967.862 968.573 968.607 968.648 968.680 968.714 968.758 968.792 17.442 18.027 17.595 17.696 17.737 17.813 17.839 17.885 17.913 17.932 18.021 18.078 18.032 18.112 18.125 18.252 18.147 18.100 17.997 17.578 17.352 17.399 17.489 17.586 17.652 17.731 17.742 17.807 17.894 17.935 18.012 17.974 17.985 18.050 18.054 18.110 18.159 18.269 18.147 17.836 17.548 17.391 17.492 17.622 17.960 18.312 17.887 17.965 18.168 18.214 18.358 18.378 18.438 18.461 18.386 18.400 18.470 18.482 18.519 18.476 18.518 18.563 18.659 18.685 18.677 18.570 18.209 17.939 17.720 17.749 17.858 18.082 18.148 18.157 18.215 18.279 18.350 18.401 18.424 18.396 18.534 18.534 18.575 18.543 18.613 18.759 18.786 17.989 17.836 17.874 17.867 17.964 18.045 18.078 18.114 18.168 17.778 17.849 17.906 17.940 18.024 18.040 18.073 18.105 18.131 18.145 18.162 18.178 18.218 18.217 18.241 18.268 18.266 18.289 18.270 18.163 17.926 17.705 17.649 17.689 17.795 17.705 17.740 17.845 17.929 17.958 18.040 18.051 18.555 18.233 18.254 18.167 18.243 18.288 18.304 18.350 18.395 18.520 18.507 18.519 18.487 18.445 18.364 18.279 18.229 18.501 18.398 18.280 18.240 18.177 18.131 18.088 18.078 18.091 18.247 18.179 18.117 18.080 18.085 18.145 18.185 18.216 18.280 18.138 18.155 18.185 18.196 18.247 18.296 18.328 17.648 17.199 17.455 17.557 17.752 17.857 17.957 18.008 18.243 18.139 17.366 17.196 17.296 17.568 17.793 17.890 17.943 18.013 18.073 18.163 18.207 18.194 18.195 18.222 18.216 18.171 17.618 17.111 17.317 17.473 17.581 17.007 16.846 16.871 16.978 16.853 16.494 16.555 16.747 16.896 16.955 16.528 16.545 16.678 16.836 16.944 16.991 16.985 16.831 16.509 16.608 16.761 16.891 16.991 16.991 16.971 16.752 16.612 16.531 16.646 16.783 16.904 16.980 16.906 16.679 16.548 16.473 16.668 16.937 16.988 16.966 16.726 16.538 17.974 18.241 18.067 17.975 18.437 18.430 18.542 18.443 18.362 18.389 18.447 18.337 18.346 18.280 18.176 18.005 18.003 18.029 18.494 18.504 18.507 18.499 18.391 18.308 18.324 18.306 18.171 18.202 18.278 18.334 18.407 18.465 18.524 18.496 18.445 18.385 18.053 17.990 18.050 18.171 18.274 18.356 18.426 18.418 18.032 18.475 18.470 17.823 18.104 18.376 18.445 18.371 18.077 18.476 18.492 18.398 18.045 17.939 17.794 17.869 18.032 18.517 18.367 18.058 17.866 17.812 17.872 18.053 18.230 18.392 18.399 18.084 17.935 17.7 77 17.890 18.196 18.389 18.449 18.475 18.020 17.899 18.039 18.250 18.433 18.516 128 Table A.7 (cont’d). NGC 6441: Photometry of the Variable Stars (B) HJ D 2450000 V71 V72 V73 V74 V75 V76 V77 V78 959.648 960.649 961.820 961.852 962.588 962.635 962.674 962.741 962.778 962.812 962.848 965.595 965.631 965.662 965.701 965.733 965.764 965.798 965.831 966.579 966.619 966.652 966.688 966.720 966.750 966.783 966.812 966.845 967.567 967.599 967.631 967.672 967.705 967.760 967.792 967.827 967.862 968.573 968.607 968.648 968.680 968.714 968.758 968.792 18.382 17.999 18.424 18.519 18.549 18.249 17.971 17.890 17.972 18.156 18.186 18.038 17.896 17.966 18.099 18.288 18.436 18.507 18.572 18.474 18.236 18.122 17.978 17.907 17.948 18.071 18.254 18.270 18.426 18.512 18.544 18.461 18.111 18.041 17.931 17.963 17.919 18.016 18.162 18.340 18.514 18.538 18.488 18.179 17.704 18.274 17.959 17.818 18.277 18.296 18.011 17.850 17.685 17.921 17.762 17.686 17.786 17.993 18.157 18.297 18.347 17.686 17.732 17.875 18.096 18.252 18.314 18.332 18.205 17.886 17.784 17.988 18.159 18.292 18.318 18.043 17.871 17.691 17.736 18.223 18.275 18.317 18.187 17.853 17.664 17.722 17.851 17.851 17.583 17.643 17.701 17.588 17.599 17.725 17.634 17.614 17.7 39 17.916 18.065 18.130 17.641 17.743 17.909 18.027 18.111 18.138 18.050 17.776 17.868 17.990 18.131 18.083 17.846 17.711 17.776 17.925 18.053 18.136 18.061 17.770 18.360 18.058 18.227 18.647 18.509 18.149 17.963 18.081 18.291 18.529 18.007 18.077 18.261 18.472 18.571 18.616 18.570 18.298 18.082 18.304 18.462 18.589 18.620 18.584 18.313 18.134 17.988 18.268 18.429 18.559 18.638 18.568 18.138 18.009 17.974 18.137 18.556 18.632 18.579 18.434 18.141 17.969 18.037 17.842 18.272 18.241 18.257 18.207 18.259 18.102 17.995 17 .906 17.836 18.076 18.005 17.862 17.785 17 .845 17.949 18.054 18.178 17.986 18.131 18.202 18.243 18.287 18.224 18.165 18.055 17.980 18.298 18.165 18.034 17.927 17.829 17.849 17.962 18.081 18.162 17.942 17.968 18.099 18.231 18.280 18.228 18.186 18.512 18.599 18.953 18.838 18.917 18.957 19.039 19.045 18.934 18.822 18.859 19.007 18.841 18.858 18.778 18.697 18.593 18.550 18.620 18.914 18.866 18.755 18.636 18.546 18.535 18.603 18.720 18.835 18.879 18.791 18.646 18.551 18.559 18.763 18.842 18.924 19.066 18.719 18.557 18.523 18.673 18.782 18.926 18.971 18.290 18.367 18.452 18.450 18.579 18.424 18.168 17.889 17.860 18.004 18.210 18.493 18.422 18.244 18.103 17.941 17.836 17.918 18.075 18.131 18.294 18.393 18.452 18.484 18.439 18.266 18.111 18.033 18.195 18.050 17.854 17.900 18.074 18.357 18.420 18.475 18.495 18.540 18.517 18.379 18.186 18.097 17.850 17.876 18.809 18.453 18.953 18.993 18.777 18.495 18.266 18.427 18.642 18.800 18.928 18.734 18.869 18.933 18.942 18.882 18.559 18.466 18.287 18.356 18.531 18.699 18.846 18.951 18.935 18.841 18.611 18.499 18.425 18.276 18.342 18.540 18.710 18.910 18.950 18.893 18.642 18.618 18.480 18.264 18.293 18.493 18.697 18.871 129 Table A.7 (cont’d). NGC 6441: Photometry of the Variable Stars (B) HJ D 2450000 V79 V80 V81 V82 V83 V84 V85 V86 959.648 960.649 961.820 961.852 962.588 962.635 962.674 962.741 962.778 962.812 962.848 965.595 965.631 965.662 965.701 965.733 965.764 965.798 965.831 966.579 966.619 966.652 966.688 966.7 20 966.750 966.783 966.812 966.845 967.567 967.599 967.631 967.672 967.705 967.760 967.792 967.827 967.862 968.573 968.607 968.648 968.680 968.714 968.758 968.792 18.390 17.952 18.356 18.148 18.451 18.268 18.049 17.835 17.789 17.935 18.210 18.084 18.067 17.821 17.775 17.895 18.057 18.236 17.830 17.991 18.162 18.299 18.419 18.425 18.479 18.445 18.261 18.433 18.485 18.430 18.284 18.108 17.948 17.802 17.819 17.976 18.022 17.869 17.768 17.834 18.024 18.198 18.326 18.341 18.696 18.249 18.272 18.392 18.269 18.222 18.273 18.317 18.390 18.506 18.563 18.553 18.543 18.461 18.373 18.330 18.278 18.235 18.556 18.430 18.351 18.292 18.231 18.240 18.219 18.267 18.316 18.360 18.288 18.258 18.224 18.267 18.363 18.445 18.552 18.634 18.249 18.276 18.387 18.428 18.506 18.605 18.620 18.700 18.776 18.687 18.660 18.797 18.690 18.697 18.750 18.771 18.845 18.754 18.722 18.714 18.683 18.681 18.738 18.791 18.858 18.704 18.768 18.799 18.865 18.963 19.041 19.016 18.923 18.847 18.996 19.063 19.031 18.933 18.806 18.699 18.693 18.688 18.718 18.778 18.706 18.662 18.650 18.651 18.677 18.734 17.399 17.598 17.475 17.413 17.424 17.355 17.342 17.379 17.461 17.533 17.437 17.395 17.374 17.361 17.376 17.407 17.472 17.527 17.557 17.603 17.580 17.502 17.448 17.388 17.361 17.350 17.359 17.368 17.368 17.390 17.415 17.461 17 .493 17.476 17.423 17.394 17.435 17.396 17.372 17.351 17.350 17.409 17.501 18.529 18.660 18.526 18.570 18.661 18.553 18.485 18.517 18.568 18.700 18.753 18.624 18.691 18.682 18.659 18.547 18.522 18.504 18.494 18.769 18.741 18.625 18.518 18.512 18.487 18.507 18.533 18.629 18.675 18.588 18.521 18.506 18.474 18.584 18.680 18.750 18.753 18.577 18.476 18.506 18.531 18.654 18.676 18.662 17.742 17.510 17.772 17.766 17.445 17.489 17.670 17.714 17.739 17.625 17.739 17.747 17.735 17.568 17.469 17.390 17.406 17.504 17.759 17.708 17.542 17.419 17.371 17.402 17.496 17.590 17.702 17.738 17.548 17.475 17.363 17.426 17.606 17.719 17.748 17.782 17.473 17.393 17.426 17.514 17.658 17.710 17.750 18.785 18.833 19.147 19.034 18.732 19.136 18.700 18.836 19.053 18.889 18.809 19.035 19.028 18.775 18.771 18.964 19.095 18.863 18.766 19.033 19.092 18.806 18.817 18.936 19.060 18.870 18.746 18.794 18.913 19.109 18.783 18.728 19.090 18.979 18.782 18.831 18.827 19.090 18.868 18.723 18.813 19.037 18.887 19.392 18.966 18.921 18.920 19.151 18.914 19.082 18.964 18.880 18.981 18.928 19.199 19.216 18.960 18.902 18.988 19.328 19.222 18.976 19.271 19.101 18.911 18.921 19.051 19.392 19.094 18.930 19.075 19.312 19.102 18.865 18.960 19.366 19.033 18.866 18.890 19.365 19.498 18.906 18.926 19.308 19.107 18.903 130 Table A.7 (cont’d). NGC 6441: Photometry of the Variable Stars (B) HJ D 2450000 V87 V88 V89 V90 V91 V92 V93 V94 959.648 960.649 961.820 961.852 962.588 962.635 962.674 962.741 962.778 962.812 962.848 965.595 965.631 965.662 965.701 965.733 965.764 965.798 965.831 966.579 966.619 966.652 966.688 966.720 966.750 966.783 966.812 966.845 967.567 967.599 967.631 967.672 967.705 967.760 967.792 967 .827 967.862 968.573 968.607 968.648 968.680 968.714 968.758 968.792 18.358 18.276 18.252 18.319 18.299 18.348 18.226 18.184 18.334 18.414 18.307 18.340 18.198 18.147 18.199 18.330 18.413 18.314 18.217 18.223 18.264 18.319 18.353 18.249 18.184 18.153 18.200 18.340 18.299 18.424 18.400 18.217 18.220 18.319 18.371 18.282 18.165 18.273 18.158 18.149 18.301 18.408 18.309 18.201 18.656 18.979 18.489 18.789 18.735 18.773 19.013 18.857 18.683 18.671 18.721 18.850 19.099 19.008 18.799 18.697 18.683 18.726 18.928 18.969 18.768 18.690 18.725 18.822 19.035 19.113 18.897 18.727 18.683 18.761 18.855 19.104 19.004 18.687 18.694 18.724 18.872 19.035 18.772 18.652 18.670 18.860 19.008 19.354 19.202 19.323 19.480 18.437 19.200 19.341 19.446 19.378 19.296 19.219 19.244 19.270 19.366 19.604 19.554 19.359 19.262 19.249 19.443 19.523 19.431 19.305 19.246 19.249 19.256 19.374 19.570 19.450 19.269 19.232 19.225 19.358 19.423 19.436 19.363 19.214 19.234 19.271 19.338 19.372 19.359 19.340 19.428 19.466 19.416 19.310 19.428 19.417 19.522 19.715 19.646 19.542 19.488 19.670 19.704 19.693 19.619 19.526 19.410 19.379 19.372 19.442 19.462 19.509 19.584 19.644 19.627 19.602 19.536 19.439 19.478 19.459 19.344 19.397 19.423 19.575 19.645 19.667 19.703 19.810 19.612 19.508 19.476 19.456 19.427 19.465 20.416 21.005 21.191 20.672 20.331 20.672 20.849 20.524 20.352 20.403 20.578 20.622 21.063 21.020 20.454 20.454 20.379 20.538 21.148 20.935 20.554 20.394 20.369 20.552 20.731 21.155 20.899 20.647 20.380 20.435 20.499 20.781 20.799 20.648 20.421 20.477 20.527 20.686 20.856 20.766 20.405 20.395 20.445 19.404 19.687 19.758 19.807 19.501 19.569 19.626 19.622 19.511 19.443 19.469 19.711 19.550 19.452 19.435 19.416 19.440 19.535 19.698 19.508 19.383 19.462 19.532 19.623 19.668 19.514 19.439 19.420 19.755 19.843 19.719 19.551 19.424 19.394 19.446 19.519 19.681 19.372 19.435 19.479 19.546 19.777 19.790 19.623 17.984 18.116 17.996 18.109 18.433 18.241 17.801 17.700 17.777 17.970 18.245 18.366 18.452 18.364 18.200 17.948 17.938 17.726 18.090 18.265 18.391 18.362 18.370 18.248 17.929 17.894 17.823 17.880 18.030 18.188 18.327 18.357 18.278 18.019 18.053 17.689 17.881 17.996 18.221 18.372 18.329 18.332 18.216 18.462 17.934 18.001 18.111 18.035 18.299 18.450 18.431 18.250 18.149 18.026 17.920 17.976 18.097 18.265 18.364 18.442 18.477 18.486 18.502 18.330 18.123 18.057 17.948 17.928 17.953 18.039 17.946 18.004 18.142 18.270 18.385 18.477 18.416 18.216 18.150 18.362 18.224 18.070 17.980 17.943 18.049 18.183 131 Table A.7 (cont’d). N GC 6441: Photometry of the Variable Stars (B) HJ D 2450000 V95 V96 V97 V98 V99 V100 V101 V102 959.648 960.649 961.820 961.852 962.588 962.635 962.674 962.741 962.778 962.812 962.848 965.595 965.631 965.662 965.701 965.733 965.764 965.798 965.831 966.579 966.619 966.652 966.688 966.720 966.750 966.783 966.812 966.845 967.567 967.599 967.631 967.672 967.705 967.760 967.792 967.827 967.862 968.573 968.607 968.648 968.680 968.714 968.758 968.792 18.279 18.438 18.377 18.554 17.965 18.131 18.507 17.923 18.413 18.245 18.392 18.471 18.075 18.431 18.160 18.249 18.483 18.004 18.377 18.542 18.098 18.453 18.190 18.203 18.517 18.083 18.319 18.366 18.579 17.891 18.418 18.357 18.442 18.318 18.214 18.488 18.500 18.256 18.327 18.555 17.925 18.491 18.153 18.553 18.518 18.738 18.777 18.611 18.715 18.677 18.715 18.714 18.697 18.614 18.577 18.554 18.526 18.534 18.508 18.534 18.571 18.506 18.541 18.558 18.542 18.574 18.585 18.648 18.628 18.676 18.565 18.624 18.642 18.619 18.655 18.647 18.698 18.724 18.728 18.624 18.696 18.746 18.739 18.732 18.783 18.454 18.369 18.449 18.454 18.380 18.444 18.453 18.502 18.508 18.525 18.470 18.391 18.376 18.311 18.320 18.255 18.291 18.284 18.324 18.300 18.280 18.283 18.326 18.327 18.350 18.354 18.386 18.332 18.359 18.352 18.353 18.392 18.426 18.458 18.482 18.488 18.453 18.426 18.483 18.521 18.527 18.525 18.586 16.706 16.678 16.690 16.676 16.634 16.656 16.676 16.675 16.685 16.667 16.665 16.568 16.589 16.596 16.591 16.589 16.597 16.589 16.594 16.530 16.550 16.570 16.581 16.580 16.570 16.574 16.560 16.568 16.506 16.536 16.535 16.546 16.548 16.530 16.545 16.543 16.532 16.480 16.480 16.508 16.508 16.514 16.498 16.512 18.370 18.335 18.433 18.453 18.431 18.482 18.471 18.453 18.465 18.468 18.462 18.535 18.558 18.582 18.583 18.575 18.586 18.579 18.572 18.588 18.603 18.605 18.604 18.606 18.612 18.617 18.611 18.629 18.649 18.626 18.613 18.631 18.647 18.638 18.653 18.664 18.654 18.635 18.689 18.660 18.729 18.693 18.704 18.714 17.763 17.729 17.737 17.757 18.811 18.771 18.518 18.179 18.000 17.921 17.860 17.743 17.722 17.768 17.729 17.729 17.672 17.732 17.716 17.737 17.716 17.718 17.744 17.738 17.708 17.697 17.715 17.756 18.892 18.848 18.705 18.468 18.269 18.025 17.912 17.834 17.817 17.747 17.685 17.707 17.731 17.716 17.675 17.708 19.343 19.056 19.245 19.267 19.271 19.298 19.301 19.296 19.272 19.297 19.287 19.330 19.319 19.282 19.312 19.247 19.256 19.308 19.266 19.351 19.362 19.356 19.381 19.404 19.380 19.362 19.381 19.420 19.271 19.325 19.281 19.285 19.305 19.263 19.318 19.330 19.333 21.301 21.415 22.270 21.384 20.299 19.826 19.642 17.126 17.282 17.158 17.221 17.430 17.209 17.103 17.208 17.321 17.396 17.368 17.436 17.459 17 .404 17.287 17.207 17.087 17.119 17.434 17.444 17.344 17.177 17.093 17.097 17.178 17.262 17.356 17.390 17.232 17.167 17.101 17.178 17.321 17.408 17.409 17.414 17.103 17.114 17.210 17.323 17.380 17.407 17.381 132 Table A.7 (cont’d). NGC 6441: Photometry of the Variable Stars (B) HJ D 2450000 V103 V104 SV10 SV11 SV12 SV13 SV14 SV15 959.648 960.649 961.820 961.852 962.588 962.635 962.674 962.741 962.778 962.812 962.848 965.595 965.631 965.662 965.701 965.733 965.764 965.798 965.831 966.579 966.619 966.652 966.688 966.720 966.750 966.783 966.812 966.845 967.567 967.599 967.631 967.672 967 .705 967.760 967.792 967.827 967.862 968.573 968.607 968.648 968.680 968.714 968.758 968.792 19.360 19.222 19.324 19.292 19.336 19.323 19.387 19.513 19.506 19.442 19.392 19.321 19.259 19.292 19.325 19.364 19.401 19.399 19.390 19.343 19.289 19.329 19.348 19.396 19.455 19.521 19.442 19.450 19.339 19.311 19.270 19.277 19.289 19.370 19.421 19.418 19.408 19.377 19.297 19.275 19.315 19.364 19.392 19.497 20.707 20.332 20.919 20.756 20.746 20.516 20.371 20.502 20.541 20.742 20.556 20.463 20.352 20.360 20.393 20.637 20.770 21.217 21.316 20.850 20.751 20.583 20.529 20.507 20.495 20.429 20.597 20.623 20.810 20.902 21.020 21.102 20.643 20.571 20.453 20.425 20.429 20.391 20.460 20.519 20.651 21.055 21.542 18.769 18.650 18.671 18.701 18.663 18.750 18.644 18.653 18.693 18.753 18.679 18.698 18.768 18.775 18.740 18.648 18.667 18.727 18.752 18.758 18.737 18.672 18.638 18.694 18.771 18.763 18.738 18.752 18.755 18.679 18.652 18.704 18.761 18.705 18.668 18.690 18.698 18.681 18.727 18.786 18.755 18.656 18.671 18.744 18.852 18.863 18.852 18.796 18.738 18.739 18.831 18.866 18.847 18.794 18.906 18.873 18.824 18.751 18.724 18.730 18.757 18.793 18.853 18.812 18.733 18.723 18.723 18.767 18.797 18.818 18.791 18.834 18.743 18.722 18.728 18.756 18.797 18.796 18.735 18.760 18.693 18.673 18.790 18.745 18.784 18.693 18.720 18.524 18.585 18.402 18.394 18.401 18.378 18.341 18.375 18.390 18.410 18.495 18.498 18.493 18.503 18.524 18.541 18.496 18.511 18.547 18.524 18.517 18.484 18.501 18.487 18.485 18.446 18.461 18.531 18.497 18.498 18.472 18.431 18.400 18.389 18.381 18.387 18.501 18.415 18.403 18.387 18.367 18.348 18.377 18.034 18.032 18.069 18.049 18.066 18.120 18.137 18.130 18.121 18.117 18.102 18.091 18.093 18.084 18.071 18.089 18.064 18.064 18.005 18.011 18.009 18.005 18.013 18.018 18.023 18.010 18.011 17.990 17.968 17.975 17.982 17.974 17.977 17.998 18.000 17.980 18.015 17.984 18.020 18.020 18.015 18.003 18.027 18.445 18.335 18.357 18.352 18.127 18.073 18.125 18.218 18.311 18.398 17.991 18.093 18.184 18.275 18.351 18.434 18.349 18.381 18.095 18.022 18.051 18.084 18.178 18.156 18.342 18.398 18.465 18.283 18.290 18.268 18.175 18.156 18.117 18.168 18.323 18.360 18.155 18.270 18.320 18.402 18.282 18.199 18.363 17.733 17.473 17.603 17.567 17.845 17.854 17 .863 17.831 17.820 17.809 17.734 17.787 17.781 17.815 17.759 17.835 17.890 17.881 17.691 17.592 17.545 17.535 17.579 17.626 17.715 17.718 17.762 17.887 17.935 17.895 17.851 17.850 17.806 17.765 17.623 17.553 17.530 17.593 17.554 17.570 17.664 17.743 17.686 133 Table A8. NGC 6388: Photometry of the Variable Stars (V) HJ D 2450000 V4 V12 V14 V16 V17 V18 V20 V21 959.676 959.741 960.616 960.716 961.805 961.840 961.872 962.569 962.622 962.660 962.720 962.762 962.798 962.834 965.580 965.618 965.650 965.688 965.720 965.752 965.784 965.817 965.850 966.566 966.598 966.639 966.671 966.707 966.738 966.770 966.831 967.555 967.586 967.618 967.650 967.692 967.747 967.780 967.811 967.849 968.561 968.593 968.626 968.667 968.699 968.740 968.778 968.811 16.433 16.459 16.499 16.525 16.601 16.574 16.587 16.615 16.611 16.631 16.622 16.644 16.627 16.648 16.777 16.796 16.799 16.804 16.808 16.818 16.815 16.811 16.816 16.836 16.863 16.856 16.861 16.857 16.868 16.865 16.868 16.887 16.898 16.908 16.907 16.924 16.924 16.918 16.921 16.926 16.950 16.962 16.970 16.989 16.981 16.986 16.996 16.994 14.608 14.594 14.586 14.593 14.570 14.574 14.565 14.554 14.533 14.513 14.447 14.488 14.475 14.491 14.461 14.438 14.454 14.483 14.464 14.464 14.471 14.465 14.447 14.407 14.408 14.393 14.427 14.415 14.425 14.481 14.478 14.389 14.366 14.369 14.366 14.370 14.369 14.396 14.403 14.362 14.373 14.358 14.354 14.390 14.386 14.378 14.384 14.379 16.104 16.090 16.108 16.091 16.093 16.098 16.100 16.130 16.125 16.107 16.084 16.083 16.081 16.086 16.237 16.462 16.797 17.213 17.035 16.628 16.346 16.168 16.114 16.119 16.107 16.108 16.120 16.150 16.172 16.207 16.174 16.136 16.118 16.112 16.110 16.119 16.193 16.408 16.744 17.174 16.094 16.097 16.086 16.085 16.085 16.083 16.096 16.114 16.944 16.762 16.984 16.809 16.801 16.912 16.988 16.845 16.970 17.005 16.816 16.731 16.770 16.858 16.833 16.936 16.989 16.988 16.897 16.771 16.746 16.793 16.878 16.797 16.862 16.958 16.998 16.955 16.837 16.758 16.813 16.772 16.830 16.900 16.972 16.990 16.819 16.745 16.761 16.847 16.778 16.823 16.899 16.982 16.986 16.860 16.751 16.748 16.698 16.754 16.256 16.504 16.192 16.246 16.383 16.552 16.523 16.604 16.719 16.761 16.732 16.853 16.457 16.509 16.533 16.567 16.632 16.687 16.704 16.726 16.759 16.867 16.580 15.986 16.029 16.157 16.262 16.336 16.489 16.662 16.696 16.733 16.705 16.793 16.857 16.833 16.669 16.060 16.281 16.392 16.474 16.506 16.570 16.585 16.633 16.675 15.281 15.276 15.479 15.507 16.042 16.011 16.035 15.365 15.277 15.244 15.208 15.264 15.204 15.283 15.302 15.286 15.266 15.296 15.310 15.313 15.307 15.297 15.297 15.556 15.582 15.528 15.540 15.554 15.587 15.621 15.662 16.036 16.039 16.039 16.008 16.029 15.989 15.940 15.925 15.929 15.327 15.336 15.354 15.349 15.355 15.361 15.369 15.348 16.584 16.799 16.693 16.860 16.851 16.765 16.753 16.892 16.880 16.930 16.892 16.805 16.723 16.693 _ 16.762 16.759 16.613 16.559 16.552 16.610 16.670 16.758 16.851 16.753 16.654 16.569 16.569 16.642 16.724 16.783 16.884 16.622 16.586 16.623 16.668 16.803 16.920 16.930 16.924 16.910 16.663 16.764 16.836 16.881 16.942 16.973 16.925 16.885 16.856 16.967 17.061 17.171 17.240 16.991 16.816 17.471 17.230 16.994 16.576 16.606 16.652 16.732 17.159 17.217 17.254 17.293 17.339 17.376 17.408 17.430 17.375 17.397 17.431 17.417 17.331 17.017 16.940 16.659 16.614 16.936 16.649 16.584 16.611 16.689 16.782 16.831 16.887 16.944 16.812 16.842 16.909 16.954 17.019 17.062 17.092 17.096 5‘; -..- 134 Table A8 (cont’d). NGC 6388: Photometry of the Variable Stars (V) HJ D 2450000 V22 V23 V26 V27 V28 V30 V31 V32 959.676 959.741 960.616 960.716 961.805 961.840 961.872 962.569 962.622 962.660 962.720 962.762 962.798 962.834 965.580 965.618 965.650 965.688 965.720 965.752 965.784 965.817 965.850 966.566 966.598 966.639 966.671 966.707 966.738 966.770 966.831 967.555 967.586 967.618 967.650 967.692 967.747 967.780 967.811 967.849 968.561 968.593 968.626 968.667 968.699 968.740 968.778 968.811 16.180 16.462 17.148 17.296 17.161 17.172 17.241 16.660 16.243 16.406 16.658 16.791 16.835 16.933 16.359 16.532 16.653 16.772 16.837 16.890 16.918 16.989 17.077 17.276 17.329 17.289 16.761 16.166 16.270 16.432 16.684 16.969 17.020 17.115 17.151 17.192 17.297 17.302 17.255 16.674 16.581 16.705 16.810 16.882 16.924 16.957 17.083 17.162 16.791 16.617 17.095 16.773 16.681 16.780 16.934 17.044 17.066 17.084 16.762 16.662 16.614 16.749 16.911 17.045 17.097 17.102 17.004 16.809 16.731 16.633 16.677 16.834 16.948 17.063 17.098 17.086 16.970 16.780 16.618 16.762 16.864 16.963 17.043 17.098 17.004 16.792 16.715 16.632 16.725 16.829 16.967 17.064 17.103 17.082 16.878 16.764 17.343 17.206 17.456 17.219 17.182 17.286 17.293 17.443 17.559 17.440 17.223 17.185 17.354 17.474 17.243 17.189 17.275 17.415 17.532 17.549 17.483 17.245 17.288 17.225 17.277 17.396 17.524 17.558 17.489 17.196 17.222 17.281 17.386 17.502 17.566 17.348 17.200 17.205 17.328 17.359 17.484 17.564 17.389 17.216 17.264 17.363 16.819 17.171 16.807 16.857 16.690 16.693 16.779 16.731 16.832 17.033 17.163 17.122 17.122 16.852 16.983 17.071 17.132 17.159 17.106 16.908 16.837 16.730 16.807 16.719 16.748 16.839 16.946 17.039 17.096 17.134 17.188 17.083 16.899 16.800 16.705 16.795 16.880 16.989 17.087 17.087 17.177 17.220 17.162 16.989 16.857 16.731 16.704 16.627 16.729 16.783 16.886 17.195 17.157 17.081 17.166 17.184 17.205 17.048 16.808 16.592 16.439 16.669 16.751 16.777 16.808 16.848 16.889 16.909 16.961 17.030 16.878 16.900 16.949 16.984 17.032 17.071 17.109 17.174 17.075 17.111 17.133 17.146 17.204 17.166 16.973 16.784 16.561 17.211 17.156 16.970 16.775 16.519 16.420 16.446 16.469 16.665 16.711 16.692 16.792 16.896 16.760 16.842 16.841 16.788 16.818 16.856 16.896 16.864 16.964 16.831 16.899 16.899 16.912 16.922 16.912 16.861 16.802 16.763 16.917 16.949 16.940 16.917 16.902 16.863 16.786 16.724 16.935 16.928 16.932 16.902 16.882 16.790 16.725 16.672 16.617 16.958 16.968 16.953 16.874 16.823 16.771 16.701 16.573 16.729 16.991 16.945 16.808 17.079 17.172 17.255 17.194 16.926 16.743 16.789 16.931 17.087 17.173 17.252 17.267 17.173 16.965 16.874 16.737 16.754 16.890 17.037 17.162 17.228 17.247 17.192 16.993 16.903 16.746 16.915 17.024 17.141 17.206 17.257 17.093 16.917 16.817 16.736 16.828 16.964 17.110 17.220 17.261 17.250 17.039 16.924 16.285 16.488 16.559 16.307 16.426 16.467 16.578 16.665 16.589 16.517 16.369 16.271 16.392 16.639 16.683 16.696 16.692 16.722 16.726 16.628 16.584 16.577 16.553 16.605 16.666 16.654 16.670 16.694 16.695 16.633 16.399 16.461 16.552 16.575 16.651 16.722 16.700 16.717 16.652 16.345 16.394 16.480 16.581 16.646 16.686 16.729 135 Table A8 (cont’d). NGC 6388: Photometry of the Variable Stars (V) HJ D 2450000 V33 V34 V35 V36 V37 V39 V40 V41 959.676 959.741 960.616 960.716 961.805 961.840 961.872 962.569 962.622 962.660 962.720 962.762 962.798 962.834 965.580 965.618 965.650 965.688 965.720 965.752 965.784 965.817 965.850 966.566 966.598 966.639 966.671 966.707 966.738 966.770 966.831 967.555 967.586 967.618 967.650 967.692 967.747 967.780 967.81 1 967.849 968.561 968.593 968.626 968.667 968.699 968.740 968.778 968.81 1 16.666 16.761 16.644 16.593 16.551 16.573 16.642 16.837 16.850 16.840 16.784 16.772 16.727 16.665 16.758 16.711 16.617 16.547 16.571 16.616 16.649 16.705 16.742 16.860 16.830 16.809 16.781 16.728 16.661 16.584 16.552 16.787 16.808 16.835 16.827 16.840 16.789 16.767 16.751 16.685 16.652 16.709 16.752 16.769 16.804 16.824 16.850 16.790 17.355 17.199 17.394 17.309 17.312 17.237 17.216 17.401 17.543 17.518 17.246 17.196 17.311 17.286 17.217 17.256 17.406 17.537 17.572 17.277 17.217 17.225 17.292 17.449 17.558 17.571 17.459 17.247 17.279 17.368 17.496 17.559 17.565 17.365 17.205 17.289 17.421 17.559 17.568 17.587 17.430 17.221 17.234 17.372 17.517 17.508 16.960 16.928 16.931 17.080 16.943 16.997 17.058 17.079 16.997 16.959 16.991 17.018 17.036 17.047 17.102 17.068 17.009 16.937 16.923 16.944 16.993 17.044 17.094 16.993 16.944 16.932 16.973 17.028 17.068 17.107 17.051 16.968 17.018 17.069 17.097 17.097 16.984 16.934 16.905 16.951 17.134 17.101 17.046 16.959 16.920 16.938 17.008 17.064 15.190 15.191 15.625 15.665 16.031 15.949 15.926 15.167 15.079 15.092 15.118 15.154 15.156 15.176 15.110 15.096 15.166 15.128 15.098 15.116 15.140 15.131 15.167 15.449 15.466 15.413 15.507 15.531 15.522 15.589 15.663 15.988 15.998 16.018 16.032 16.065 16.155 16.108 16.124 16.169 15.184 15.142 15.140 15.150 15.097 15.108 15.111 15.120 136 14.681 14.715 14.762 14.784 14.747 14.753 14.730 14.929 14.759 14.722 14.737 14.697 14.586 14.730 14.723 14.680 14.731 14.595 14.702 14.706 14.720 14.548 14.474 14.580 14.625 14.551 14.456 14.467 14.459 14.594 14.669 14.594 14.502 14.510 14.471 14.557 14.536 14.561 14.534 14.472 14.659 14.594 14.608 14.601 14.591 14.577 14.600 14.624 18.162 18.511 18.158 18.183 18.507 18.197 18.108 18.226 18.530 18.229 18.103 18.161 18.284 18.440 18.101 18.111 18.161 18.348 18.379 18.244 18.180 18.155 18.193 18.279 18.213 18.174 18.182 18.342 18.556 18.239 18.102 18.569 18.305 18.178 18.103 18.161 18.377 18.373 18.230 18.165 18.320 18.411 18.262 18.163 18.173 18.237 18.497 18.386 18.027 17.962 17.984 18.008 17.968 17.927 17.892 17.966 18.166 17.944 17.871 17.887 17.921 17.924 17.926 17.948 18.007 18.143 18.136 18.009 17.879 17.999 17.967 17.920 17.895 17.928 18.038 18.149 18.118 18.003 18.014 18.016 18.012 17.974 17.925 17.911 17.943 18.005 18.743 18.743 18.712 18.919 19.052 18.804 18.688 18.907 18.751 18.665 18.903 18.886 18.662 18.647 18.754 18.656 18.705 18.910 18.813 18.683 18.678 18.790 19.035 18.682 18.776 18.883 18.709 18.644 18.712 18.960 18.721 18.887 18.784 18.673 18.653 18.851 18.827 18.665 18.650 18.826 18.681 18.731 18.905 19.030 18.756 18.664 18.806 18.977 Table A8 (cont’d). NGC 6388: Photometry of the Variable Stars (V) HJ D 2450000 V42 V43 V44 V45 V46 V47 V48 V49 959.676 959.741 960.616 960.716 961.805 961.840 961.872 962.569 962.622 962.660 962.720 962.762 962.798 962.834 965.580 965.618 965.650 965.688 965.720 965.752 965.784 965.817 965.850 966.566 966.598 966.639 966.671 966.7 07 966.738 966.770 966.831 967.555 967.586 967.618 967.650 967.692 967.747 967.780 967.81 1 967.849 968.561 968.593 968.626 968.667 968.699 968.740 968.778 968.811 17.132 17.113 17.171 17.187 17.162 17.164 17.183 17.168 17.172 17.171 17.122 17.129 17.117 17.110 17.113 17.125 17.113 17.126 17.125 18.365 19.000 19.290 18.880 18.225 17.805 17.490 17.204 17.158 17.156 17.146 17.150 17.161 17.152 17.144 17.142 17.168 17.203 17.193 17.184 17.165 17.162 17.169 17.153 17.144 15.670 15.661 15.665 15.673 15.668 15.685 15.678 15.678 15.685 15.671 15.822 15.990 16.118 16.121 15.664 15.676 15.667 15.660 15.658 15.660 15.662 15.666 15.662 15.673 15.669 15.663 15.663 15.664 15.664 15.662 15.666 15.670 15.665 15.666 15.664 15.661 15.659 15.658 15.663 15.666 15.665 15.666 15.672 15.664 15.664 15.670 15.665 15.659 19.369 19.372 19.863 19.440 19.422 19.377 19.386 20.506 19.936 19.621 19.403 19.415 19.359 19.418 19.556 19.490 19.479 19.449 19.423 19.420 19.396 19.402 19.390 20.259 20.417 20.197 19.828 19.530 19.413 19.367 19.377 19.547 19.532 19.541 19.528 19.461 19.391 19.379 19.404 19.391 20.127 20.336 20.604 20.047 19.751 19.498 19.456 19.492 18.169 18.050 17.978 18.181 17.782 18.181 18.077 18.256 17.992 18.259 18.177 17.742 18.170 18.031 17.962 18.241 17.789 18.213 17.846 18.113 18.240 17.897 18.216 18.242 18.001 18.155 18.173 18.036 18.246 17.777 18.174 18.164 18.033 18.271 17.770 18.231 18.037 18.255 17.802 18.204 18.142 18.209 18.026 18.272 17.909 18.276 17.877 18.242 16.755 16.757 16.775 16.814 16.862 16.879 16.866 16.886 16.917 16.925 16.929 16.928 16.931 16.918 17.042 17.062 17.081 17.077 17.082 17.083 17.088 17.090 17.079 17.099 17.114 17.118 17.128 17.147 17.131 17.137 17.135 17.127 17.161 17.167 17.187 17.177 17.182 17.187 17.178 17.188 17.181 17.192 17.195 17.199 17.211 17.218 17.199 17.187 15.244 15.256 15.238 15.259 15.249 15.221 15.227 15.213 15.200 15.211 15.183 15.189 15.193 15.218 15.124 15.146 15.160 15.159 15.157 15.161 15.170 15.155 15.134 15.100 15.118 15.094 15.128 15.117 15.113 15.157 15.186 15.084 15.070 15.088 15.084 15.092 15.088 15.114 15.114 15.074 15.073 15.089 15.106 15.111 15.109 15.113 15.112 15.089 16.157 16.161 16.134 16.157 16.130 16.133 16.130 16.088 16.125 16.111 16.124 16.123 16.123 16.113 16.043 16.050 16.063 16.063 16.061 16.062 16.060 16.054 16.056 16.020 16.028 16.038 16.046 16.047 16.049 16.043 16.032 16.001 16.015 16.018 16.022 16.025 16.033 16.024 16.026 16.015 15.993 15.995 16.006 16.012 16.014 16.017 16.007 16.004 16.572 16.557 16.323 16.605 16.675 16.631 16.651 16.831 16.594 16.506 16.403 16.522 16.471 16.702 16.333 16.492 16.553 16.623 16.692 16.702 16.629 16.549 16.539 16.541 16.477 16.423 16.451 16.522 16.602 16.634 16.660 16.736 16.616 16.482 16.396 16.407 16.567 ‘ 16.559 16.600 16.707 16.698 16.774 16.779 16.506 16.528 16.381 16.426 16.297 137 Table A8 (cont’d). NGC 6388: Photometry of the Variable Stars (V) HJ D 2450000 V50 V51 V52 V53 V54 V55 V56 V57 V58 959.676 959.741 960.616 960.716 961.805 961.840 961.872 962.569 962.622 962.660 962.720 962.762 962.798 962.834 965.580 965.618 965.650 965.688 965.720 965.752 965.784 965.817 965.850 966.566 966.598 966.639 966.671 966.707 966.738 966.770 966.831 967.555 967.586 967.618 967.650 967.692 967.747 967.780 967.811 967.849 968.561 968.593 968.626 968.667 968.699 968.740 968.778 968.811 17.044 16.872 16.656 16.986 16.763 16.857 16.971 16.863 16.958 17.041 17.155 17.126 16.869 16.892 16.615 16.686 16.759 16.898 17.006 17.108 17.075 17.085 17.027 17.182 17.173 16.962 16.845 16.717 16.620 16.633 16.837 16.737 16.855 16.958 17.024 17.160 17.191 16.940 16.825 16.770 16.945 16.926 16.827 16.679 16.754 16.900 17.023 17.069 16.672 16.892 16.832 16.626 16.611 16.568 16.731 16.745 16.843 17.014 17.159 17.172 16.886 16.905 16.977 17.115 17.120 17.069 16.898 16.838 16.608 16.618 16.720 16.703 16.802 16.957 17.003 17.088 17.144 17.026 16.789 16.884 16.810 16.616 16.613 16.784 17.004 17.042 17.074 17.144 17.183 17.115 16.978 16.793 16.666 16.612 16.765 16.781 16.558 16.451 16.372 16.704 16.436 16.471 16.603 16.396 16.478 16.592 16.713 16.763 16.743 16.706 16.706 16.636 16.559 16.474 16.414 16.393 16.452 16.553 16.644 16.418 16.522 16.630 16.715 16.740 16.764 16.742 16.569 16.773 16.716 16.562 16.574 16.443 16.427 16.472 16.591 16.671 16.427 16.538 16.626 16.631 16.724 16.704 16.662 16.545 16.624 16.369 16.852 16.829 16.836 16.823 16.912 16.913 16.691 16.617 16.522 16.473 16.551 16.753 16.846 16.853 16.765 16.802 16.775 16.669 16.620 16.792 16.654 16.592 16.558 16.541 16.590 16.706 16.873 16.768 16.856 16.870 16.965 16.911 16.651 16.640 16.570 16.522 16.611 16.498 16.472 16.412 16.532 16.919 16.879 16.985 16.917 16.818 16.730 16.731 17.011 16.930 16.930 16.850 16.824 16.773 16.759 16.932 16.925 16.889 16.843 16.816 16.789 16.742 16.716 16.706 16.966 16.939 16.870 16.833 16.812 16.781 16.756 16.712 16.972 16.927 16.888 16.830 16.813 16.769 16.725 16.705 16.688 16.951 16.929 16.881 16.842 16.813 16.759 16.733 16.678 19.092 19.837 19.389 19.177 19.313 19.079 19.225 19.303 19.527 19.886 19.365 19.219 19.275 19.643 19.870 19.673 19.360 19.225 19.233 19.449 19.752 19.388 19.220 19.380 19.240 19.336 19.714 19.821 19.359 19.231 19.364 19.347 19.582 19.690 19.374 19.219 19.404 19.898 19.598 19.282 19.610 19.271 19.286 19.392 19.704 19.442 19.217 19.174 16.616 16.766 16.547 16.743 16.819 16.862 16.839 16.629 16.730 16.724 16.836 16.882 16.905 16.873 16.704 16.794 16.838 16.880 16.930 16.938 16.895 16.837 16.765 16.726 16.810 16.905 16.893 16.930 16.946 16.879 16.726 16.779 16.842 16.879 16.884 16.906 16.869 16.847 16.752 16.754 16.852 16.846 16.866 16.887 16.876 16.870 16.826 16.776 16.671 16.798 16.680 16.710 16.732 16.653 16.738 17.079 16.842 16.838 16.826 16.761 16.599 16.661 16.592 16.641 16.652 16.755 16.774 16.857 16.820 16.884 16.950 16.878 16.847 16.677 16.593 16.631 16.666 16.689 16.748 16.927 16.903 16.859 16.803 16.798 16.690 16.577 16.603 16.677 16.907 17.019 17.066 17.052 17.009 16.948 16.882 16.740 18.950 19.115 18.892 19.291 19.664 19.092 18.931 18.862 19.376 18.902 19.189 19.190 18.901 19.221 18.892 18.929 19.439 19.349 18.981 18.895 19.109 19.393 19.109 18.938 18.989 19.440 19.027 18.871 18.969 19.393 18.883 18.892 19.085 19.614 19.018 18.946 19.397 19.120 18.883 18.832 19.020 19.441 18.958 18.904 19.226 19.403 19.006 138 Table A9. NGC 6388: Photometry of the Variable Stars (B) HJ D 2450000 V4 V12 V14 V16 V17 V18 V20 V21 959.687 959.750 960.624 961.814 961.847 962.561 962.602 962.651 962.692 962.709 962.733 962.769 962.806 962.842 965.573 965.610 965.642 965.695 965.728 965.760 965.792 965.824 965.858 966.558 966.590 966.631 966.663 966.700 966.745 966.778 966.839 967.562 967.594 967.626 967.658 967.699 967.740 967.772 967.803 967.841 968.550 968.585 968.619 968.659 968.692 968.753 968.786 968.819 18.183 18.215 18.265 18.287 18.319 18.326 18.341 18.361 18.362 18.357 18.375 18.386 18.377 18.373 18.556 18.505 18.531 18.536 18.543 18.537 18.548 18.543 18.539 18.615 18.584 18.579 18.576 18.562 18.584 18.571 18.583 18.589 18.647 18.598 18.613 18.636 18.636 18.645 18.630 18.621 18.648 18.655 18.686 18.742 18.658 18.729 18.732 18.743 16.512 16.490 16.479 16.506 16.473 16.430 16.425 16.498 16.488 16.482 16.494 16.486 16.497 16.467 16.350 16.408 16.437 16.427 16.422 16.439 16.423 16.408 16.407 16.362 16.375 16.404 16.419 16.416 16.396 16.436 16.422 16.347 16.366 16.371 16.371 16.376 16.370 16.368 16.366 16.353 16.299 16.327 16.344 16.343 16.336 16.354 16.319 16.311 16.634 16.639 16.653 16.630 16.645 16.666 16.657 16.626 16.629 16.630 16.620 16.619 16.613 16.627 16.737 16.947 17.290 17.892 17.515 17.111 16.820 16.666 16.647 16.655 16.640 16.638 16.650 16.649 16.675 16.690 16.685 16.658 16.643 16.646 16.640 16.637 16.687 16.871 17.217 17.744 16.661 16.632 16.622 16.620 16.615 16.626 16.621 16.643 17.488 17.294 17.592 17.371 17.507 17.406 17.476 17.598 17.516 17.432 17.321 17.254 17.337 17.454 17.383 17.494 17.584 17.561 17.428 17.286 17.291 17.352 17.473 17.313 17.402 17.517 17.581 17.558 17.348 17.281 17.387 17.298 17.389 17.486 17.570 17.574 17.397 17.293 17.278 17.377 17.298 17.353 17.445 17.573 17.585 17.359 17.275 17.302 17.469 17.536 16.900 16.701 16.844 17.260 17.270 17.324 17.475 17.519 17.528 17.574 17.668 17.650 17.081 17.203 17.282 17.334 17.408 17.541 17.517 17.546 17.625 17.687 17.406 16.513 16.514 16.692 16.916 17.097 17.273 17.475 17.544 17.564 17.550 17.618 17.628 17.659 17.502 16.812 16.816 16.968 17.105 17.212 17.257 17.351 17.392 17.464 16.014 16.035 16.469 17.137 17.181 16.097 16.021 16.042 16.046 16.063 16.089 16.105 16.090 16.130 16.047 16.059 16.070 16.112 16.128 16.127 16.136 16.166 16.178 16.608 16.618 16.622 16.625 16.659 16.673 16.699 16.743 17.227 17.227 17.216 17.190 17.171 17.118 17.032 16.970 16.988 16.099 16.134 16.160 16.141 16.170 16.214 16.209 16.218 17.067 17.260 17.118 17.281 17.205 17.344 17.393 17.454 17.438 17.399 17.337 17.259 17.224 17.088 17.234 17.220 17.096 16.970 16.982 17.080 17.187 17.297 17.385 17.229 17.089 17.006 16.998 17.099 17.237 17.384 17.451 17.028 17.019 17.073 17.171 17.296 17.381 17.418 17.462 17.435 17.053 17.172 17.284 17.358 17.402 17.442 17.389 17.290 17.632 17.780 17.885 17.959 17.694 18.397 18.217 17.719 17.375 17.219 17.997 18.054 18.116 18.189 18.225 18.288 18.317 18.304 18.174 18.322 18.337 18.339 18.217 17.913 17.552 17.210 17.221 17.542 17.211 17.184 17.232 17.348 17.881 17.542 17.611 17.712 17.474 17.556 17.648 17.742 17.772 17.881 17.940 17.958 139 Table A9 (cont’d). NGC 6388: Photometry of the Variable Stars (B) HJ D 2450000 V22 V23 V26 V27 V28 V30 V31 V32 959.687 959. 750 960.624 961.814 961.847 962.561 962.602 962.651 962.692 962.709 962.733 962.769 962.806 962.842 965.573 965.610 965.642 965.695 965.728 965.760 965.792 965.824 965.858 966.558 966.590 966.631 966.663 966.700 966. 745 966.778 966.839 967.562 967.594 967 .626 967.658 967.699 967.740 967.772 967.803 967.841 968.550 968.585 968.619 968.659 968.692 968.753 968.786 968.819 16.663 17.060 18.023 17.953 18.026 17.512 16.640 16.894 17.136 17.241 17.375 17.518 17.621 17.719 16.832 17.054 17.249 17.514 17.587 17.643 17.725 17.811 17.965 18.170 18.202 18.174 17.609 16.605 16.776 16.998 17.367 17.782 17.873 17.990 18.020 18.023 18.133 18.182 18.150 17.507 17.131 17.342 17.500 17.649 17.678 17.810 17.916 18.052 17.270 17.055 17.725 17.172 17.368 17.600 17.688 17.738 17.493 17.328 17.281 17.102 17.094 17.274 17.443 17.629 17.698 17.709 17.517 17.289 17.171 17.079 17.175 17.337 17.507 17.656 17.708 17.717 17.453 17.280 17.078 17.279 17.428 17.587 17.686 17.725 17.627 17.333 17.230 17.092 17.162 17.316 17.511 17.648 17.719 17.622 17.327 17.237 17.646 17.925 17.693 17.654 17.684 17.774 17.925 18.151 18.164 18.101 17.884 17.693 17.728 17.942 18.110 17.765 17.684 17.854 18.012 18.155 18.148 18.007 17.736 17.866 17.728 17.781 17.922 18.106 18.160 18.013 17.661 17.734 17.820 17.975 18.123 18.169 17.956 17.711 17.674 17.840 17.833 17.976 18.167 18.172 17.989 17.675 17.767 17.917 17.415 17.847 17.350 17.200 17.342 17.254 17.401 17.595 17.696 17.779 17.865 17.865 17.715 17.419 17.597 17.714 17.850 17.833 17.719 17.473 17.399 17.243 17.436 17.265 17.263 17.384 17.562 17.731 17.813 17.786 17.878 17.668 17.450 17.341 17.208 17.300 17.450 17.593 17.761 17.715 17.810 17.891 17.821 17.605 17.337 17.217 17.231 17.420 17.692 17.695 18.087 18.104 18.135 18.131 18.142 18.132 18.048 17.832 17.593 17.224 17.076 17.468 17.520 17.584 17.701 17.719 17.764 17.812 17.891 17.976 17.742 17.792 17.799 17.872 17.935 18.009 18.021 18.103 18.026 18.082 18.076 18.120 18.163 18.120 17.872 17.546 17.343 18.215 18.134 17.875 17.587 17.264 17.068 17.185 17.272 17.540 17.647 17.622 17.727 17.785 17.678 17.742 17.748 17.772 17.794 17.838 17.838 17.844 17.886 17.755 17.811 17.819 17.864 17.852 17.832 17.740 17.648 17.587 17.852 17.873 17.875 17.875 17.851 17.757 17.603 17.512 17.881 17.894 17.868 17.825 17.742 17.619 17.571 17.482 17.408 17.873 17.905 17.849 17.755 17.635 17.535 17.440 17.377 17.240 17.583 17.481 17.690 17.797 17.916 17.509 17.376 17.284 17.225 17.317 17.544 17.747 17.762 17.873 17.909 17.751 17.461 17.362 17.203 17.271 17.475 17.616 17.748 17.879 17.908 17.867 17.495 17.405 17.239 17.501 17.653 17.804 17.881 17.892 17.745 17.477 17.376 17.219 17.317 17.485 17.662 17.825 17.914 17.813 17.528 17.441 16.850 17.123 17.160 16.958 17.114 17.456 17.423 17.257 17.198 17.181 17.073 16.874 16.834 16.961 17.285 17.360 17.366 17.405 17.387 17.366 17.257 17.217 17.179 17.167 17.254 17.310 17.353 17.357 17.371 17.365 17.256 16.983 17.092 17.195 17.263 17.325 17.379 17.378 17.390 17.382 16.894 16.914 17.000 17.151 17.247 17.330 17.401 17.434 140 Table A.9 (cont’d). NGC 6388: Photometry of the Variable Stars (B) HJ D 2450000 V33 V34 V35 V36 V37 V38 V39 V40 959.687 959.750 960.624 961.814 961.847 962.561 962.602 962.651 962.692 962.709 962.733 962.769 962.806 962.842 965.573 965.610 965.642 965.695 965.728 965.760 965.792 965.824 965.858 966.558 966.590 966.631 966.663 966.700 966.745 966.778 966.839 967.562 967.594 967.626 967.658 967.699 967.740 967.772 967.803 967.841 968.550 968.585 968.619 968.659 968.692 968.753 968.786 968.819 17.400 17.516 17.301 17.187 17.631 17.648 17.618 17.563 17.554 17.548 17.519 17.451 17.338 17.501 17.429 17.319 17.208 17.251 17.317 17.397 17.466 17.524 17.670 17.604 17.553 17.530 17.473 17.332 17.212 17.221 17.566 17.600 17.627 17.635 17.604 17.555 17.514 17.491 17.419 17.358 17.407 17.472 17.512 17.555 17.629 17.608 17.574 17.787 17.747 17.920 17.767 17.673 17.716 17.820 18.139 18.182 18.170 18.027 17.752 17.719 17.889 17.891 17.709 17.735 18.024 18.166 18.206 18.068 17.768 17.721 17.753 17.806 18.005 18.148 18.195 17.937 17.757 17.846 17.970 18.131 18.213 18.168 17.810 17.700 17.769 17.952 18.169 18.205 18.235 18.110 17.774 17.684 17.988 18.134 18.135 17.469 17.475 17.437 17.476 17.554 17.629 17.569 17.507 17.523 17.528 17.539 17.560 17.588 17.584 17.685 17.643 17.587 17.467 17.450 17.474 17.551 17.615 17.661 17.569 17.475 17.450 17.490 17.563 17.651 17.669 17.577 17.513 17.581 17.644 17.677 17.668 17.574 17.486 17.438 17.464 17.691 17.695 17.633 17.521 17.449 17.488 17.577 17.649 15.901 15.977 16.631 16.879 16.839 15.868 15.840 15.830 15.851 15.868 15.885 15.899 15.919 15.982 15.752 15.760 15.759 15.790 15.778 15.807 15.830 15.844 15.871 16.375 16.383 16.396 16.412 16.441 16.477 16.493 16.544 17.033 17.028 17.036 17.048 17.087 17.128 17.147 17.182 17.204 15.865 15.835 15.818 15.796 15.789 15.793 15.798 15.842 15.824 15.859 15.970 16.017 16.003 16.168 16.110 16.091 16.107 16.118 16.109 16.089 16.093 16.120 15.799 15.798 15.797 15.808 15.789 15.789 15.773 15.766 15.772 15.737 15.735 15.706 15.694 15.701 15.681 15.714 15.699 15.693 15.692 15.680 15.664 15.661 15.686 15.685 15.675 15.678 15.732 15.767 15.779 15.765 15.772 15.767 15.741 15.726 16.428 16.884 16.278 16.299 16.068 16.108 16.108 16.153 16.155 16.160 16.182 16.182 16.186 16.244 16.313 16.237 16.159 16.042 15.936 15.807 15.663 15.530 15.443 16.216 16.241 16.242 16.241 16.268 16.298 16.507 16.320 16.377 16.052 15.958 15.825 15.661 14.487 14.415 15.375 15.415 15.279 16.305 16.345 16.298 16.369 16.435 16.403 16.313 19.295 19.583 19.290 19.527 19.260 19.342 19.587 19.408 19.240 19.228 19.226 19.296 19.475 19.505 19.184 19.205 19.273 19.506 19.426 19.348 19.242 19.234 19.325 19.433 19.357 19.246 19.287 19.417 19.613 19.316 19.191 19.790 19.429 19.251 19.203 19.279 19.441 19.531 19.351 19.289 19.297 19.509 19.467 19.355 19.242 19.360 19.686 19.420 18.810 18.677 18.747 18.779 18.761 18.762 18.738 18.699 18.662 18.737 18.951 18.901 18.706 18.652 18.666 18.722 18.742 18.682 18.686 18.755 18.901 18.879 18.744 18.626 18.794 18.736 18.687 18.691 18.689 18.779 18.902 18.956 18.813 18.810 18.777 18.781 18.733 18.680 18.696 18.753 18.791 141 Table A9 (cont’d). NGC 6388: Photometry of the Variable Stars (B) HJ D 2450000 V41 V42 V43 V44 V45 V46 V47 V48 959.687 959.750 960.624 961.814 961.847 962.561 962.602 962.651 962.692 962.709 962.733 962.769 962.806 962.842 965.573 965.610 965.642 965.695 965.728 965.760 965.792 965.824 965.858 966.558 966.590 966.631 966.663 966.700 966.745 966.778 966.839 967.562 967.594 967.626 967.658 967.699 967.740 967.772 967.803 967.841 968.550 968.585 968.619 968.659 968.692 968.753 968.786 968.819 19.866 19.934 19.840 20.119 19.794 20.005 20.000 19.771 19.851 20.017 20.186 19.957 19.793 19.837 19.958 19.811 19.776 20.022 19.922 19.765 19.802 19.965 20.142 19.753 19.808 20.045 19.877 19.724 19.825 20.159 19.781 20.009 19.842 19.803 19.754 20.079 20.003 19.830 19.705 19.890 19.772 19.783 20.071 20.139 20.010 19.929 20.048 20.154 17.781 17.841 17.777 17.800 17.781 17.779 17.798 17.800 17.781 17.779 17.798 17.790 17.804 17.789 17.789 17.776 17.773 17.775 17.762 17.769 17.775 17.779 17.773 19.049 19.840 20.588 20.162 19.189 18.432 18.073 17.789 17.821 17.794 17.785 17.784 17.762 17.781 17.781 17.776 17.783 17.848 17.831 17.803 17.788 17.775 17.792 17.774 17.788 16.647 16.636 16.621 16.645 16.642 16.666 16.663 16.651 16.710 16.764 16.860 17.052 17.160 17.144 16.638 16.646 16.644 16.641 16.639 16.635 16.638 16.647 16.644 16.662 16.658 16.645 16.643 16.641 16.646 16.642 16.641 16.650 16.647 16.643 16.641 16.638 16.643 16.643 16.641 16.637 16.664 16.647 16.652 16.651 16.650 16.648 16.645 16.645 20.321 20.359 20.618 20.190 20.245 21.550 21.227 20.660 20.288 20.372 20.263 20.308 20.226 20.232 20.335 20.348 20.251 20.269 20.235 20.228 20.224 20.223 20.267 21.145 21.610 21.214 20.905 20.446 20.206 20.238 20.183 20.298 20.306 20.244 20.326 20.359 20.289 20.262 20.253 20.252 20.834 21.740 21.412 21.256 20.667 20.292 20.312 20.410 18.828 18.726 18.661 18.406 18.836 18.835 18.218 18.871 18.377 18.662 18.882 18.307 18.828 18.217 18.345 18.835 18.246 18.857 18.203 18.765 18.739 18.572 18.885 18.780 18.804 18.683 18.858 18.452 18.849 18.422 18.481 18.338 18.715 18.875 18.390 18.874 18.440 18.847 18.239 18.773 18.663 18.863 18.422 18.858 18.265 18.749 18.559 18.861 18.712 18.745 18.675 18.829 18.819 18.791 18.862 18.860 18.882 18.870 18.872 18.860 18.863 18.822 18.990 18.988 19.004 19.009 19.017 19.036 19.008 19.026 19.029 18.970 19.007 19.063 19.051 19.079 19.063 19.094 19.090 19.060 19.077 19.081 19.111 19.116 19.097 19.126 19.112 19.111 19.064 19.141 19.121 19.148 19.132 19.138 19.146 19.059 17.262 17.258 17.238 17.225 17.232 17.203 17.203 17.230 17.240 17.252 17.250 17.254 17.252 17.251 17.105 17.150 17.163 17.169 17.158 17.171 17.165 17.167 17.154 17.095 17.124 17.139 17.140 17.140 17.130 17.157 17.127 17.084 17.101 17.103 17.107 17.107 17.124 17.128 17.104 17.097 17.048 17.074 17.100 17.111 17.112 17.115 17.109 17.108 17.980 17.985 17.971 17.978 17.978 17.921 17.964 17.949 17.963 17.973 17.963 17.961 17.946 17.960 17.900 17.893 17.896 17.916 17.902 17.914 17.903 17.908 17.898 17.887 17.883 17.905 17.906 17.899 17.890 17.899 17.871 17.864 17.857 17.886 17.877 17.874 17.893 17.893 17.889 17.872 17.844 17.868 17.861 17.888 17.881 17.872 17.878 17.858 142 Table A9 (cont’d). NGC 6388: Photometry of the Variable Stars (B) HJ D 2450000 V49 V50 V51 V52 V53 V54 V55 V56 959.687 959.750 960.624 961.814 961.847 962.561 962.602 962.651 962.692 962.709 962.733 962.769 962.806 962.842 965.573 965.610 965.642 965.695 965.728 965.760 965.792 965.824 965.858 966.558 966.590 966.631 966.663 966.700 966.745 966.778 966.839 967.562 967.594 967.626 967.658 967.699 967.740 967.772 967.803 967.841 968.550 968.585 968.619 968.659 968.692 968.753 968.786 968.819 17.064 17.055 17.091 17.098 17.175 17.159 16.993 16.839 16.796 16.833 17.000 17.101 17.223 16.704 16.884 17.014 17.120 17.139 17.207 17.130 16.990 16.983 16.990 16.879 16.829 16.892 17.021 17.136 17.166 17.179 17.209 17.040 16.948 16.848 16.830 16.929 17.021 17.078 17.170 17.148 17.141 17.152 16.904 16.887 16.782 16.781 16.776 17.781 17.509 17.282 17.298 17.563 17.404 17.583 17.753 17.857 17.917 17.904 17.777 17.484 17.484 17.244 17.225 17.308 17.645 17.763 17.822 17.868 17.809 17.618 17.959 17.900 17.623 17.453 17.329 17.138 17.184 17.497 17.375 17.522 17.676 17.792 17.877 17.920 17.692 17.437 17.397 17.685 17.561 17.396 17.245 17.251 17.571 17.777 17.845 17.690 17.737 17.665 17.238 17.497 17.803 17.891 18.046 18.196 18.303 18.336 18.206 17.759 17.769 18.164 18.463 18.264 18.186 17.849 17.619 17.374 17.347 17.487 17.549 17.692 17.921 17.996 18.144 18.185 17.902 17.572 17.862 17.635 17.440 17.499 17.695 18.014 18.151 18.213 18.191 18.491 18.725 18.382 17.802 17.640 17.490 17.337 17.352 17.221 17.053 17.042 17.252 17.053 17.103 17.333 17.412 17.454 17.583 17.495 17.474 17.404 17.288 17.166 17.051 17.197 17.375 17.106 17.206 17.429 17.300 17.071 17.202 17.497 17.584 17.272 17.300 17.071 17.115 17.202 17.343 17.497 17.104 17.212 17.392 17.439 17.491 17.582 17.315 17.180 17.608 17.566 17.490 17.577 17.668 17.496 17.395 17.289 17.188 17.085 17.083 17.095 17.356 17.537 17.517 17.586 17.605 17.431 17.318 17.231 17.546 17.340 17.240 17.144 17.120 17.258 17.418 17.621 17.481 17.580 17.661 17.691 17.614 17.347 17.256 17.171 17.079 17.347 17.158 17.075 17.002 17.163 17.438 17.747 17.653 17.817 17.530 17.496 17.853 17.800 17.778 17.700 17.684 17.651 17.599 17.544 17.496 17.789 17.761 17.708 17.630 17.553 17.551 17.507 17.462 17.441 17.822 17.774 17.704 17.639 17.593 17.534 17.490 17.444 17.796 17.752 17.689 17.627 17.570 17.532 17.482 17.443 17.432 17.779 17.754 17.680 17.617 17.584 17.501 17.473 17.448 20.089 20.605 20.231 20.065 20.079 20.304 20.007 20.650 20.505 20.231 20.137 20.042 20.153 20.573 20.320 20.801 20.140 19.953 20.175 20.454 20.582 20.184 20.091 20.329 20.103 20.086 20.388 20.858 20.237 20.017 20.222 20.165 20.512 20.479 20.178 20.077 20.229 20.683 20.650 20.195 20.547 20.246 20.077 20.197 20.680 20.204 20.122 20.060 17.244 17.464 17.206 17.549 17.566 17.268 17.197 17.344 17.499 17.538 17.546 17.602 17.589 17.576 17.359 17.444 17.534 17.615 17.664 17.622 17.572 17.495 17.372 17.416 17.482 17.570 17.632 17.663 17.649 17.575 17.388 17.466 17.559 17.582 17.620 17.626 17.613 17.536 17.400 17.388 17.510 17.611 17.630 17.667 17.630 17.570 17.484 17.445 143 Table A9 (cont’d). NGC 6388: Photometry of the Variable Stars (B) HJ D 2450000 V57 V58 959.687 959.750 960.624 961.814 961.847 962.561 962.602 962.651 962.692 962.709 962.733 962.769 962.806 962.842 965.573 965.610 965.642 965.695 965.728 965.760 965.792 965.824 965.858 966.558 966.590 966.631 966.663 966.700 966.745 966.7 78 966.839 967.562 967.594 967.626 967.658 967.699 967.740 967.772 967.803 967.841 968.550 968.585 968.619 968.659 968.692 968.753 968.786 968.819 17.443 17.718 17.320 17.281 17.412 17.771 17.669 17.571 17.493 17.479 17.479 17.359 17.216 17.309 17.296 17.276 17.297 17.498 17.559 17.554 17.633 17.654 17.664 17.564 17.538 17.315 17.198 17.218 17.308 17.331 17.436 17.628 17.587 17.535 17.505 17.434 17.356 17.220 17.229 17.315 17.677 17.766 17.844 17.892 17.718 17.651 17.675 17.615 20.115 20.247 19.863 20.794 20.073 19.973 20.692 19.991 20.031 20.024 20.421 20.216 19.959 20.418 20.007 19.993 20.789 20.333 19.989 20.026 20.313 20.285 20.372 20.028 20.082 20.490 20.124 19.943 20.086 20.312 19.988 20.013 20.304 20.735 20.025 20.040 20.346 20.298 19.942 20.011 20.1 13 20.524 20.042 19.901 20.778 20.368 20.047 144 APPENDIX B ADDITIONAL FIGURES 145 Figure B1 The field of NGC 6441. North is down, east is left. 146 v - o ‘ ‘ Z .'. I . ' I O Q . O I 0 . ' - - . .v - . . . I ‘- ‘ " . . o ‘ ° I . 7 . . U. . . «I . a O . . a O ' ‘ I ‘ ‘ a ‘ I ... . I: o . _ 5.. E I ' . . . .0 : f u . ‘ . . . I o 5 I ' . I . II J ' ' .. . a. '7‘ . o I . ‘ I . 0 . . . I . t- . .; ° ‘ . . ° 0- o 4 1 c 3'! o I 6 ¢ I ‘o . . - '- .‘. ‘. . a . . . . ' On . ‘ 9 ~ ‘ u i s ‘ . '0 5 o . I . . h 7 I O - Q . I . ‘ . ’ . . . . I . - . . . . '0'. ‘I- ‘ . . . N . . -‘ .0 . . I . ' d ~ . . ”8 i ‘. ' ' I ‘ 0‘ o . v ’7". . ~ . . . . g-) ‘ ‘ I v . . . . l o o 9 f I . ‘ . . ‘ . ‘ . . .1 .. _ i ' . ‘0 . . . - ' . o I ' ‘ Q Q a I . . .‘ " - . s o . . I a. g I " . O Q . . ' . ‘ ' . “I. c \ .- (3.. .0 ' Figure B.2a The southeast quadrant of NGC 6441. North is down, east is left. 147 Figure B.2b. The northeast quadrant of NGC 6441. North is down, east is left. 148 Figure B.2c. The northwest quadrant of NGC 6441. North is down, east is left. 149 Figure B.2d. The southwest quadrant of NGC 6441. North is down, east is left. 150 NGC 6441. f region 0 Figure 3.38.. The core 151 Figure B.3b. The core region of NGC 6441. 152 Figure B.3c. The core region of NGC 6441. 153 - _‘ o .0 -. .. I O 9 . a I Figure B.3d. The core region of NGC 6441. 154 Figure B.3e. The core region of NGC 6441. 155 . o . P . I ‘ u ' o a . . .- I I ' o. O ‘ - ’ . I o . b g 0‘ I I ‘ . . O o ' ‘ ‘ , § 0 . 0 . .- . O o I p O I n o . a r o o O . o ‘ ' o . ‘ I .0 . I . . n . I ‘ . I . . o g. . I v I ' . 0 t 1 0 ‘ . - .'. . .o' . . . ° 1 ' _ I D x o . ' . Q . . o . O O . I . I 0 l ' a I a. l- I . o s . I o t _ O _ .l ‘ I t o . I c I A I. l C u o I o C so 0 C I ‘ u . .~ O I o I O I , . . 3 I . . I 0 u . I a . . i. O 1‘ ' a . I . O 0 ~ . . Q 0 ~ ' o ' ' I ‘ ‘ I. a . ' o ‘ \ o o ' o . D . u . I .0 I . ' . I . A .‘ O o . . O ' . . u ' I . I . . o o t ' O 2' . I . ' o .‘o 7. 9 . . a ' o . I O .’ . o O . . o ' ' I I .. . O . I ‘ _ o . . 6 _ . o , C Figure 8.4. The field of NGC 6388. North is down, east is left. 156 '- 10 ' t‘ q 0 ' o ‘D I .. O '_ a '. C u o ,1 O. b Figure 3.58.. The southeast quadrant of NGC 6388. North is down, east is left. 157 Figure B.5b. The northeast quadrant of NGC 6388. North is down, east is left. 158 Figure B.5c. The northwest quadrant of NGC 6388. North is down, east is left. 159 ‘ . J ' O O ‘0 ‘0 , :- ' o _ ' ' o . . .. .I . I . . o. _ . . . ..- . I ‘ ‘ ;‘ O o' O ‘ n o I. ' o . 1 o .D I . O ‘ I I o ' .. . . ' o . ‘ O .3 - 1 I ' ‘ C 0' ‘ b 6 .- . ° I ' . ' O , I a Figure B.5d. The southwest quadrant of NGC 6388. North is down, east is left. 160 Figure B.6a. The core region of NGC 6388. 161 Figure B.6b. The core region of NGC 6388. 162 o . . Figure B.6c. 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